Solvent-mediated hydrodynamic interactions play an important role in understanding the behavior of many soft materials. However, modeling the solvent at process-relevant scales is challenging due to its significantly smaller size than the suspended materials. Multiparticle collision dynamics (MPCD) is a mesoscopic, particle-based solvent model that can flexibly address this challenge. Some of us previously developed highly performant, open-source MPCD software in HOOMD-blue with parallelization for both CPUs and GPUs. Here, we highlight report on new developments to this software aimed at expanding the capabilities of MPCD for simulating bulk shear rheology. Specifically, we have generalized the MPCD algorithm to support deformed simulation boxes and corresponding MPCD collision cells in order to efficiently enable Lees–Edwards shear-flow boundary conditions. We have characterized how deforming the simulation box affects transport properties of the MPCD solvent and embedded solutes. In the process, we have also refactored the collision-cell calculations and domain decomposition used in MPCD in HOOMD-blue to improve performance, and we report updated benchmarks for our software on modern CPU and GPU resources. These developments will enable new studies of shear rheology in complex fluids while maintaining good computational performance.