Yes, you can mix these approaches. Almost every client-server game does that to some extent, e.g. Unreal Engine 1, 2 and 3 supports both replicated state and re

Yes, you can mix these approaches. Almost every client-server game does that to some extent, e.g. Unreal Engine 1, 2 and 3 supports both replicated state and replicated function calls, although it's mostly based on state replication. However, even a small amount of constant error with lock-step networking means that you can't distribute the authority. Imagine a case where a unit is low on health and a tiny error in the unit's position makes the difference between whether it's out of range or in range of an enemy unit's fire. Thus it either lives or dies based on the presence of absence of that error. With fully deterministic lock-step networking, a client can make that determination on its own, without checking in with anyone else for confirmation. Without perfect determinism, the best it can do is make a tentative decision, which it might have to reverse soon thereafter if the server's view of the situation disagrees.