  A typical working condition in the study of quantum quenches is that the
initial state produces a distribution of quasiparticle excitations with an
opposite-momentum-pair structure. In this work we investigate the dynamical and
stationary properties of the entanglement entropy after a quench from initial
states which do not have such structure: instead of pairs of excitations they
generate $\nu$-plets of correlated excitations with $\nu>2$. Our study is
carried out focusing on a system of non-interacting fermions on the lattice. We
study the time evolution of the entanglement entropy showing that the standard
semiclassical formula is not applicable. We propose a suitable generalisation
which correctly describes the entanglement entropy evolution and perfectly
matches numerical data. We finally consider the relation between the
thermodynamic entropy of the stationary state and the diagonal entropy, showing
that when there is no pair structure their ratio depends on the details of the
initial state and lies generically between $1/2$ and $1$.
