In this paper, we build on this approach, as well as engineering optimization literature and our OpenFF Evaluator software, to introduce a multi-fidelity optimization framework based on the construction of Gaussian process (GP) surrogate models that simultaneously approximate the response surface of many physical properties with respect to changes in the LJ parameters. Using the accelerated objective evaluation offered by the surrogates, we implement a global optimization algorithm to search broadly and propose candidate parameter sets. We then validate these parameter sets by evaluating the objective at the simulation level, accepting candidates in good agreement. Iterating between global optimization over the surrogate, and simulation-level validation and surrogate refinement, we can drive the optimizer to explore promising regions of parameter space with a limited number of simulation evaluations.