There's no Apple-approved way to edit the existing keyboard. If you want them to allow it, file a feature request.
That said, it just so happens that in most applications the keyboard (instance of UIKeyboard) is a separate UIWindow, and you can iterate over the windows in the application and start adding custom subviews that respond to the appropriate touch actions. Find it by iterating over [[UIApplication sharedApplication] windows] and checking to see if the description contains the string UIKeyboard. For more info on this method and some sample code, see this answer.
Another approach is to create your own custom view and build a keyboard from scratch. Be careful if you do this, though, as it requires a lot of manual work, not only in creating the keyboard and getting the touch behavior to match Apple's, but also in any control you add that would bring up the regular keyboard - you'll need to redirect things like becomeFirstResponder to show your own keyboard, rather than Apple's.
Edit: As ZaBlanc pointed out, newer versions of iOS have a way to do this with the inputView and inputAccessoryView properties. See the UIResponder class reference for details.