We investigate a composite quantum collision model with measurements on the memory
part, which effectively probe the system. The framework allows us to adjust the measurement
strength, thereby tuning the dynamical map of the system. For a two-qubit setup with a symmetric
and informationally complete measurement on the memory, we study the divisibility of the resulting
dynamics in dependence of the measurement strength. The measurements give rise to quantum
trajectories of the system and we show that the average asymptotic purity depends on the specific
form of the measurement. With the help of numerical simulations, we demonstrate that the different
performance of the measurements is generic and holds for almost all interaction gates between the
system and the memory in the composite collision model. The discrete model is then extended to a
time-continuous limit