Being flexible and able to handle multiple types of data is exactly what method overloading and interfaces were created for. Java already has the features that make handling these situations simpler while guarenteeing compile time safety via type checking.

Also, if it is impossible to narrowly define what data the method operates on, then that method may be doing too much and needs to be decomposed into smaller methods.

I like a rule of thumb I've read about (in Code Complete I think). The rule states that you should be able to tell what a function or method does just by reading its name. If it is really difficult to clearly name a function\method using that idea (or have to use And in the name) then the function/method is really doing too much.