  We introduce a one-dimensional (1D) pseudospin model on a ladder where the
Ising interactions along the legs and along the rungs alternate between
$X_{i}X_{i+1}$ and $Z_{i}Z_{i+1}$ for even/odd bond (rung). We include also the
next nearest neighbor Ising interactions on plaquettes' diagonals that
alternate in such a way that a model where only leg interactions are switched
on is equivalent to the one when only the diagonal ones are present. Thus in
the absence of rung interactions the model can interpolate between two 1D
compass models. The model posses local symmetries which are the parities within
each $2\times 2$ cell (plaquette) of the ladder. We find that for different
values of the interaction it can realize ground states that differ by the
patterns formed by these local parities. By exact diagonalization we derive
detailed phase diagrams for small systems of $L=4$, 6 and 8 plaquettes, and use
next $L=12$ to identify generic phases that appear in larger systems as well.
Among them we find a nematic phase with macroscopic degeneracy when the leg and
diagonal interactions are equal and the rung interactions are larger than a
critical value. The nematic phase is similar to the one found in the
two-dimensional compass model. For particular parameters the low-energy sector
of the present plaquette model reduces to a 1D compass model with spins $S=1$
which suggests that it realizes peculiar crossovers within the class of compass
models. Finally, we show that the model can realize phases with broken
translation invariance which can be either dimerized, trimerized,
\textit{etcetera}, or completely disordered and highly entangled in a~well
identified window of the phase diagram.
