Mutation of integrator

Suppose that I use an explicit scheme with fixed time-stepping to integrate an ODE, and I am not interested in interpolations of any sort.

Is it ok to change directly the right-hand-side function f, the state u and the time t in between the steps (provided that I use low-level integrator interface)?

Yup, if you don’t care about the interpolations then this should be good. Set u_modified!(integrator,true) when you do so that way it knows the recompute a few things.