Q:

Add to a javascript function

I have a function I can't modify:
function addToMe() { doStuff(); }

Can I add to this function? Obviously this syntax is terribly wrong but it's the general idea...
function addToMe() { addToMe() + doOtherStuff(); }

A:

You could store a reference to the original function, and then override it, with a function that calls back the original one, and adds the functionality you desire:
var originalFn = addToMe;

addToMe = function () {
  originalFn(); // call the original function
  // other stuff
};

You can do this because JavaScript functions are first-class objects.
Edit: If your function receives arguments, you should use apply to pass them to the original function:
addToMe = function () {
  originalFn.apply(this, arguments); // preserve the arguments
  // other stuff
};

You could also use an auto-executing function expression with an argument to store the reference of the original function, I think it is a little bit cleaner:
addToMe = (function (originalFn) {
  return function () {
    originalFn.apply(originalFn, arguments); // call the original function
    // other stuff
  };
})(addToMe); // pass the reference of the original function

