The quasi-particle picture is a powerful tool to understand the entanglement spreading in many-body quantum systems after a quench.
As an input, the structure of the excitations' pattern of the initial state must be provided,
the common choice being pairwise-created excitations.
However, several cases exile this simple assumption.
In this work we investigate weakly-interacting to free quenches in one dimension.
This results in a far richer excitations' pattern where multiplets with a larger number of particles are excited.
We generalize the quasi-particle ansatz to such a wide class of initial states,
providing a small-coupling expansion of the Rényi entropies.
Our results are in perfect agreement with iTEBD numerical simulations.