Plato's theory has an extremely wide scope - it is aimed at addressing a number of fundamental metaphysical questions including:
- how do we explain resemblance?
- the problem of universals (the question of whether properties exist, and if so, what they are)?
- what do we mean by matter and substance?
- what is change?
The argument for the existence of Forms seems to be abductive, inference to the best explanation.
The key issue for me in debating Forms is to try and understand what Plato actually thinks they are, this is not an easy question!