Is there a class of all classes? If not, can I define the “banana” so we have the “banana” of all classes? Is there a banana of all bananas? If I define an apple of all bananas, is there an apple of all apples. Can this go on indefinitely? Does mathematics make any sense doing this?

If I take the limit of such a process, do I get everything, ever?

Edit: If you are going to downvote, at least explain why. This is a legitimate question.