We describe an efficient and scalable framework for modeling crosstalk effects on quantum information processors. By applying optimal control techniques, we show how to tune-up arbitrary high-fidelity parallel operations on systems with substantial local and nonlocal crosstalk. As an example, we simulate a 2D square array of 100 superconducting transmon qubits. These results suggest that rather than striving to engineer away undesirable interactions during fabrication, we can largely mitigate such effects with software through careful characterization and control optimization.