I'm not sure if this will still be useful to people, but with ES6 I have a way to do it that I find clean and useful.
class MyClass {
constructor ( arg1, arg2, arg3 )
myFunction1 () {...}
myFunction2 () {...}
myFunction3 () {...}
}
module.exports = ( arg1, arg2, arg3 ) => { return new MyClass( arg1,arg2,arg3 ) }
And then you get your expected behaviour.
var MyClass = require('/MyClass.js')( arg1, arg2, arg3 )