If you really believe that the A/B parameter space and the C/D parameter space interact with each other, then yes, you could get stuck in a local minimum. So in that case you should test all combinations simultaneously. However, it will take a lot longer to collect enough data in this case. So if you think it is likely that the parameters are independent, it would be better to change only one set at a time.
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If you really believe that the A/B parameter space and the C/D parameter space interact with each other, then yes, you could get stuck in a local minimum. So in that case you should test all combinations simultaneously. However, it will take a lot longer to collect enough data in this case. So if you think it is likely that the parameters are independent, it would be better to change only one set at a time.