Relative free energy (RFE) calculations are now widely used in academia and the industry, but their accuracy is often limited by poor sampling of the complexes' conformational ensemble. To help address conformational sampling problems when simulating many relative binding free energies, we developed a novel method termed multiple topology replica exchange of expanded ensembles (MT-REXEE). This method enables parallel expanded ensemble calculations, facilitating iterative RFE computations while allowing conformational exchange between parallel transformations. These iterative transformations can be adaptable to any set of systems with a common backbone or central substructure. We demonstrate that the MT-REXEE method maintains thermodynamic cycle closure to the same extent as standard expanded ensemble calculations for both solvation free energy and relative binding free energy calculations. The transformations tested involve systems that incorporate diverse heavy atoms and multisite perturbations of a small molecule core resembling multisite λ dynamics, without necessitating modifications to the MD code. Our initial implementation is in GROMACS. We outline a systematic approach for the topology setup and provide instructions on how to perform inter-replica coordinate modifications. This work shows that MT-REXEE can be used to perform accurate and reproducible free energy estimates and prompts expansion to more complex test systems and other molecular dynamics simulation infrastructures.