A link from this post (at How does philosophy study the world?) brought to mind the following line of thought: the definition of Metaphilosophy (not to be confused with the SE website, which incidentally only examines a narrow aspect [viz., questions] of the broader subfield of philosophy) provided in that link was the study of what philosophy is, what philosophy is for, how philosophy should be done, and in general, the study of the nature of philosophy as a discipline. But if I replace each occurrence of the word "philosophy" in that definition with the word "metaphilosophy", I would assume that the new definition that I would have come up with would now be the definition of "meta-metaphilosophy", which would study metaphilosophy in a manner similar to the way that metaphilosophy studies philosophy. My question then is how far, from a practical standpoint, can my "replacement" process be carried out? That is, how many "metas-" (as prefixes) can be put in front of "philosophy" before inquiry into the study of it becomes practically impossible? Or is there such a limit? Or am I simply mistaken about the plausibility of the "process" that I'm proposing here?
There are no theoretical limits to the "level" of metaphilosophy, but in practice, on or two levels suffice most of the time for two reasons: 1. A further level of reflections does not produce any new insights, 2. A further level of reflection leads into another field of metaphilosophy, that already works on "level one" of metaphilosophy.
Ad 1) Take Epistemology for example. One question is: How can we gain knowledge about the outter world? Kant's groundbreaking answer to this was a meta-philosophical turn (a transcendental argument): What are the conditions of possibility to know anything at all? Kant thus explained the conditions for gaining knowledge about the world by reflecting on the process of gaining knowledge. So, could we go a level deeper (or higher) in meta-philosophy? The according question would be: What are the conditions of possibility for thinking about the conditions of possibility to know anything at all? It starts to get complicated, but we could still manage. But it turns out, that the conditions for possibility for thinking are not that different form the conditions of possibility for knowing, i.e. assumption of the categories "time" and "causality" (to focus on one aspect). Would you gain any new insight, if you took the question one step further? What are the conditions of possibility for thinking about the conditions of possibility for thinking about the conditions of possibility to know anything at all? In Kantian reasoning, you would come to the same answer as with the last question: The necessity of the categories of time and causality.
Ad 2) Meta-Ethics reflects on the way we talk about ethics. What are the deontological markers we ascribe to an action (should, ought to, must not, ...) and how do they interact? When do we frame a certain kind of moral problem as a dilemma? What's dilemmatic about a moral dilemma? Take the last question: Here you would try to produce some criteria that must apply to a situation for it to be a moral dilemma, possibly with the help of examples or analogies. Now, let's get metaphysical and ask the following question: How do we know we are right, when we are wondering whether a certain situation is a moral dilemma? So you are reflecting on reflecting on moral dilemmata. What do you wish to gain from this question? Maybe you are looking for some sort of framework that allows you to reflect on moral dilemmata and that tells you when your reasoning was successful. So what you are really asking is: When is my theory about moral dilemmata plausible? But this relates to philosophy of science: What are criteria for a good theory? Much work has been done on the quality (and the nature) of a scientific theory, and you could draw on this work when questioning your own reasoning about moral dilemmata.
Meta-philosophy is a powerful tool. Yet, while there are no theoretical limits to it, practically you will either ask the same question again, or you will come to another field of (meta-)philosophy (like philosophy of science, argumentation theory, logic,...).