  The emergence of clustering and coarsening in crowded ensembles of
self-propelled agents is studied using a lattice model in one-dimension. The
persistent exclusion process, where particles move at directions that change
randomly at a low tumble rate $\alpha$, is extended allowing sites to be
occupied by more than one particle, with a maximum $n_\text{max}$ per site.
Three phases are distinguished. For $n_\text{max}=1$ a gas of clusters form,
with sizes distributed exponentially and no coarsening takes place. For
$n_\text{max}\geq 3$ and small values of $\alpha$, coarsening takes place and
few large clusters appear, with a large fraction of the total number of
particles in them. In the same range of $n_\text{max}$ but for larger values of
$\alpha$, a gas phase where a negligible fraction of particles takes part of
clusters. Finally, $n_\text{max}=2$ corresponds to a crossover phase. The
character of the transitions between phases is studied extending the model to
allow $n_\text{max}$ to take real values and jumps to an occupied site are
probabilistic. The transition from the gas of clusters to the coarsening phase
is continuous and the mass of the large clusters grows continuously when
varying the maximum occupancy, and the crossover found corresponds to values
close to the transition. The second transition, from the coarsening to the
gaseous phase can be either continuous or discontinuous depending on the
parameters, with a critical point separating both cases.
