Philosophers through history have done many researches on "a priori" concepts and ideas, the most influential one today might be Kant, but of course many influential philosophers have taken such approach to philosophizing about the nature of the world (mainly; it may be that philosophers has used such approach to other areas too, but I'm not sure I'm aware of any).
The key limit that I seem to grasp from this approach is the intellectual imagination of the philosopher (and most of the times also logic, but, as many philosophers takes this approach to also explore the logic system itself I'm not sure if we should call it exactly a limit). A philosopher can go on with his research purely on his imagination (and of course the accepted philosophy will also most of the time require a big amount of rationality in it too; but that, as well as logic, isn't exactly a limit).
My question is, are there any other limits to the a priori research "method" (probably calling it a method is a false assumption, as there isn't exactly a method, or at least not only one, to do such research, but I'll use it for the readability of the question) except the imagination of the philosopher? For contrast, a postriori research, will have at least the limits of the experience, of the evidence, of the "real" (in the philosophical use of the word) world.