map limit with promises. play with it here: https://jsbin.com/fazihoc

mapLimit.js

function eachN(arr, n) {
    const arr0 = arr.slice();
    const arrs = [];
    while (arr0.length > 0) {
        arrs.push( arr0.splice(0, n) );
    }
    return arrs;
}

function mapLimit(arr, promFn, limit) {
    const arrs = eachN(arr, limit);
    let results = [];
    return new Promise(function(resolve, reject) {
        function step() {
            const batch = arrs.shift();
            if (!batch) { return resolve(results); }
            Promise.all(batch.map(promFn))
                .then(function(subRes) {
                    results = results.concat(subRes);
                    step();
                })
                .catch(function(err) {
                    reject(err);
                });
        }
        step();
    });
}

usage-example.js

function sleep(ms) {
    return new Promise(resolve => setTimeout(resolve, ms));
}

function sleep2(n) {
    return new Promise(resolve => {
        console.log('FIRED ' + n);
        sleep(500).then(() => {console.log(n); resolve(n); });
    });
}

mapLimit([1,2,3,4,5,6,7], sleep2, 3).then(r => console.log(r));

I just play with your idea, check this: https://gist.github.com/Anmo/cdf674e09644f24ea58bef327e8016b3