The most practical thing to do would be ride your Schwinn until you've worn some stuff out. (Might not take that long) But if you really want to upgrade and have a clear final idea of what you want to end up with, I see no reason why you couldn't replace parts and then eventually buy a new frame. Then, move all your new parts over to the new frame. You could save some money this way if you keep your eye out for deals on parts and get lucky.