Developing an optimizing compiler backend remains a laborious process, especially for nontraditional ISAs that have been appearing recently. Superoptimization sidesteps the need for many code transformations by searching for the most optimal instruction sequence semantically equivalent to the original code fragment. Even though superoptimization discovers the best machine-specific code optimizations, it has yet to become widely-used. We propose GreenThumb, an extensible framework that reduces the cost of constructing superoptimizers and provides a fast search algorithm that can be reused for any ISA, exploiting the unique strengths of enumerative, stochastic, and symbolic (SAT-solver-based) search algorithms. To extend GreenThumb to a new ISA, it is only necessary to implement an emulator for the ISA and provide some ISA-specific search utility functions. This paper demonstrates retargetability of GreenThumb by showing how to construct a superoptimizer for a small subset of LLVM IR.