Within the context of optimal quantum control, the solution to a gate synthesis problem can depend on several continuous parameters. We present a framework which allows learning parametrized gates that can be tuned to high fidelity across a large number and wide range of continuous parameter values. We refer to our method as Single-Optimization Multiple-Application (SOMA). This kind of learning can be understood as an instance of meta-optimization or trajectory learning, that is finding a solution for an optimizer which itself finds a solution to problem instances.