It seems clear that Newton's first law is a special case of his second. Although perhaps people might argue that it emphasizes the centrality of inertial frames.
But is the third law also just a special case of the second? Could a physical system exist which obeyed the first two laws but not the third? Or does the third again simply emphasize an aspect of the second that is useful didactically?
Responding to a comment about why the third is a subset of the second, take an example of an object sitting on a table. The object has gravity pulling down but it is not accelerating so the net force must be 0 (from N2). Similar logic can be applied to other situations (I think). At least, that's what this question is trying to clarify.