request-module-handler.js

var request = require('request')
request.on('init', function(er) {console.log('starting')})
request.on('initialized', function(er) {console.log('ready to go')})
request.on('error', function(er) {console.log('first error handler')})
var z = request.on('error', function(er) { console.log('second error handler')}).get('aaa');

request-module-handler.out

starting
first error handler
second error handler
ready to go