  We consider stationary stochastic processes arising from dynamical systems by
evaluating a given observable along the orbits of the system. We focus on the
extremal behaviour of the process, which is related to the entrance in certain
regions of the phase space, which correspond to neighbourhoods of the maximal
set $\mathcal M$, i.e. the set of points where the observable is maximised. The
main novelty here is the fact that we consider that the set $\mathcal M$ may
have a countable number of points, which are associated by belonging to the
orbit of a certain point, and may have accumulation points. In order to prove
the existence of distributional limits and study the intensity of clustering,
given by the Extremal Index, we generalise the conditions previously introduced
in \cite{FFT12,FFT15}.
