Definitely. Two fairly standard techniques in mathematics are solving a cut down version of a problem and lifting that to a full solution, and solving a more general version and specializing to a particular case. Sometimes, amazingly, the more general problem is easier to solve, perhaps because fewer irrelevant details stand in the way.

Both methods have yielded a lot of progress in mathematics. For example, solving a cut down version of Fermat’s Last Theorem got us the theory of ideals in algebra. Relatedly, Wiles work on the modularity theorem ultimately led to the actual proof of FLT.