So, I've begun looking at Plato's theory of forms. The wikipedia article says that every table on the earth has a certain "tableness" to them. However, I would say that circular tables have a certain circular tableness to them as well as a tableness. In fact I might say (being an Object-Oriented programmer) that circular tableness itself has a certain tableness to it. In this case, could Plato's theory of forms also apply to Plato's forms themselves?
I dont think so. Plato almost certainly wasn't thinking like an OOP.
Forms themselves don't exist physically. They are abstract, and not in the weak sense that they are merely fuzzy, or not fully defined, Forms are abstract in the strong sense in that they are conceptually pure, irreducible, and non-material. a form cannot have multiple attributes, since, at least in some sense, forms are attributes.
part of the description Plato gives of the form of beauty is that it is:
but itself by itself with itself 
he later says that a form neither receives into itself anything else from anywhere else, nor itself enters into anything anywhere. Think of it like prime factoring a number; 27 becomes 3*3*3, 3*9 equals 27 as well, but as 9 is reducible to 3*3, we can say that 9 receives into itself 3*3. On the other hand, 3 or indeed any prime number, only remains a form while it is not functioning in any way (such as in 3*3 or even just as the symbol 3), since forms also do not enter into anything anywhere.
So in the case of the example you give, there can't exist a form such as 'circular tableness' because it lacks the quality of being irreducible. I'd argue that 'circular tableness' is actually a concept, not a form, and that it is itself an instance of the forms circle and table.
further, I don't think there is such a thing as the form of a form, firstly just on an historical basis, plato is one of the most widely known philosophers in the history of the world, so we can assume he was a fairly accomplished logician, I cant imagine he would have been blind to such an obvious infinite regression (form, form of a form, form of a form of a form, etc) so I think its more likely that on Plato's view its not the case that forms express various qualities like tableness and blueness, rather there are things that are tableness and blueness, which plato calls forms because they are irreducible (where 'being irreducible' is not a property possessed by the form, but a description that applies to it.)
Yes, you can say that forms themselves have corresponding forms. This is the basis of the Third Man Argument against the Theory of Forms, which was presented by Plato himself through the mouth of a young Socrates in the dialogue Parmenides. There's no established interpretation of the meaning of Plato's arguments against what's supposed to be his own theory, nor a established interpretation of the overall dialogue, a thorny and puzzling reading.
See Plato's Parmenides, from the Stanford's Encyclopedia of Philosophy.