  We consider the dynamics of a collisional model in which both the system and
environment are embodied by spin-$1/2$ particles. In order to include
non-Markovian features in our model we introduce interactions among the
environmental qubits and investigate the effect that different models of such
interaction have on the degree of non-Markovianity of the system's dynamics. By
extending that interaction beyond the nearest-neighbour, we enhance the degree
of non-Markovianity in the system's dynamics. A further significant increase
can be observed if a collective interaction with the forthcoming environmental
qubits is considered. However, the observed degree of non-Markovianity in this
case is non-monotonic with the increasing number of qubits included in the
interaction. Moreover, one can establish a connection between the degree of
non-Markovianity in the evolution of the system and the fading behaviour of
quantum coherence in its state as the number of collisions grow. We complement
our study with an investigation on system-environment correlations and present
an example of their importance on a physical upper bound on the trace distance
derivative.
