Suppose I have an object X defined as
var X = function () {};
X.prototype.doSomething = function () {};
X.prototype.doSomethingElse = function (
No, it is not possible (in a standard way). Every possibility to create a callable object (i.e., a function) will create one inheriting from Function.prototype1; and you can't change the [[prototype]] of an object afterwards2.
See also:
1: OK, ES6 allows us to subclass Function. But that's not as useful as it sounds.
2: Since ES6, you can use Object.setPrototypeOf.