The interplay between martensitic phase transformations and plastic slip in crystalline materials gives rise to intricate microstructures, which, from a variational perspective, originate from highly nonconvex energy functionals. In this context, we study a prototypical variational model in finite crystal plasticity with a single slip system. In contrast to classical settings with a single elastic well, the elastic energy here features two wells, which leads to a coupling between plastic slip and the elastic phases under different compatibility constraints. To understand the effective deformation behavior, we analyze the relaxation of this model, with a focus on the quasiconvexification of the underlying extended-valued energy densities. First, we identify the quasiconvex hull of the set of admissible deformation gradients, showing that the macroscopically attainable states cover a range of volumetric responses. We then derive rank-one convex upper and polyconvex lower bounds on the quasiconvex envelope. In certain regimes, these bounds coincide and a convex integration argument shows that they agree with the quasiconvex envelope. This is joint work with Elisa Davoli and Samuele Ricco (TU Wien).