Oibackoff typing that works thanks to a bug that makes things simpler!

generator-v3.ts

import * as fs from 'fs';

// Settings
let generics = ['a','b'];
let maxParameters = 10;
let maxCallbackParameters = 2;
let parameterName = 'data';

// File
let fileStream = fs.createWriteStream('index.d.ts');

// Generate the instance
let lines: string[] = [];
for (let maxGeneric = 1; maxGeneric <= generics.length; maxGeneric++) {
    let genericNotation = `<${generics.slice(0, maxGeneric).map(v => v.toUpperCase()).join(',')}>`;
    let functionCallbackNotation = `callback: (${generics.slice(0, maxGeneric).map(v => `${v}: ${v.toUpperCase()}`).join(', ')}) => any`;
    let callbackNotation = `callback: (${generics.slice(0, maxGeneric).map(v => `${v}: ${v.toUpperCase()}`).join(', ')}, ${maxGeneric < 2 ? 'data: null, ' : ''}priorErrors?: ${generics[0].toUpperCase()}[]) => void`;

    // Loop through each allowed amount of backoff parameters
    for (let maxBackoffParamNumber = 0; maxBackoffParamNumber < maxParameters; maxBackoffParamNumber++) {
        
        // Build the list of backoff parameters
        let backoffParams: string[] = [];
        for (let backoffParamNumber = 0; backoffParamNumber < maxBackoffParamNumber; backoffParamNumber++) {
            backoffParams.push(`${parameterName}${backoffParamNumber}: any`)
        }

        // Loop through each allowed amount of callback parameters
        for (let maxCallbackParamNumber = 0; maxCallbackParamNumber < maxCallbackParameters; maxCallbackParamNumber++) {

            // Build the list of callback parameters
            let callbackParams: string[] = [];
            for (let callbackParamNumber = 0; callbackParamNumber < maxCallbackParamNumber; callbackParamNumber++) {
                callbackParams.push(`${parameterName}${callbackParamNumber}: any`)
            }
            callbackParams.push(functionCallbackNotation);

            let immediateArgs: string[] = [];
            immediateArgs.push(`fn: (${callbackParams.join(', ')}) => any`)
            immediateArgs = immediateArgs.concat(backoffParams);
            immediateArgs.push('intermediate: BackoffIntermediate<A>');
            immediateArgs.push(callbackNotation);
            lines.push(`${genericNotation}(${immediateArgs.join(', ')}): void;`)

            let noImmediateArgs: string[] = [];
            noImmediateArgs.push(`fn: (${callbackParams.join(', ')}) => any`)
            noImmediateArgs = noImmediateArgs.concat(backoffParams);
            noImmediateArgs.push(callbackNotation);
            lines.push(`${genericNotation}(${noImmediateArgs.join(', ')}): void;`)
        }

    }
}
fileStream.write(`export declare interface BackoffInstance {\n    ${lines.join('\n    ')}\n}\n`);

index.d.ts

export declare interface BackoffInstance {
    <A>(fn: (callback: (a: A) => any) => any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, data2: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, data2: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, data2: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, data2: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, data8: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, data8: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, data8: any, intermediate: BackoffIntermediate<A>, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A>(fn: (data0: any, callback: (a: A) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, data8: any, callback: (a: A, data: null, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, data8: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, data8: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, data8: any, intermediate: BackoffIntermediate<A>, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
    <A,B>(fn: (data0: any, callback: (a: A, b: B) => any) => any, data0: any, data1: any, data2: any, data3: any, data4: any, data5: any, data6: any, data7: any, data8: any, callback: (a: A, b: B, priorErrors?: A[]) => void): void;
}