I'm not sure I understand the question fully, so let me see if I can sharpen it up a little bit.
Is your question: Is there a set of possible answers that could in principle be given to any given philosophical question?
If that's your question the answer is No. Different kinds of problems are going to have different kinds of possible answers that could be given to them.
The space of possible answers is probably smallest in logic. One kind of question that comes up in logic is: Can one create a formal system with property P? And there the answer is either yes or no. But it also often happens that there is a question like Does claim p follow from axioms a, b, and c in system s? and there there are three possible answers that might be given: provably yes *provably no* or undecidable.
In metaphysics it gets much more complicated. Take the question of free will and determinism that you mention. Some people might want to say there's not really a question worth trying to figure here. There are two different ways to make an argument like that:
Deflationists could say that the question is really just verbal, there isn't a substantial disagreement here, only a kind of misuse of language leading to a pseudo problem.
Mysterians could say that the question is meaningful and perhaps even has an answer but it is an answer nobody in principle could know because of the cognitive limitations of the human mind.
I don't know that these two kinds of solutions could in principle be given for any metaphysical topic, but certainly they are common (deflationism much more so than mysterianism). However, if one thinks there is a meaningful, substantive question at stake in the free will debate and that it is in principle answerable, then there are a number of possible positions. There are actually at least three distinct questions involved here Does moral responsibility require the freedom of will? and Is the freedom of the will compatible with determinism? and Is determinism actually true? At first glance it looks like the answers to these three questions must be either yes or no, so we should expect 2^3 different possible positions. In practice the most common are:
- libertarianism (responsibility requires freedom, freedom isn't compatible with determinism, but determinism is false),
- hard compatibilism (responsibility requires freedom, freedom is compatible with determinism, determinism is true),
- soft compatibilism (responsibility requires freedom, freedom is compatible with determinism, determinism is false),
- hard determinism (responsibility requires freedom, freedom is not compatible with determinism, determinism is true),
- reactive attitudes (responsibility does not require freedom, freedom is not compatible with determinism, determinism is true)
These are different substantive positions on the free will issue. Each different metaphysical problem (what are laws of nature? what are numbers? how do dispositions work?) will have a variety of different substantive positions like this, and I don't see any common features those answers share that would allow us to categorize them any more specifically.