Partial methods play an important role in formal methods and beyond. Recently such methods were developed for parity games, where polynomial-time partial solvers decide the winners of a subset of nodes. We investigate here how effective polynomial-time partial solvers can be by studying interactions of partial solvers based on generic composition patterns that preserve polynomial-time computability. We show that use of such composition patterns discovers new partial solvers - including those that merge node sets that have the same but unknown winner - by studying games that composed partial solvers can neither solve nor simplify. We experimentally validate that this data-driven approach to refinement leads to polynomial-time partial solvers that can solve all standard benchmarks of structured games. For one of these polynomial-time partial solvers not even a sole random game from a few billion random games of varying configuration was found that it won't solve completely.