  We characterize the post-inflationary dynamics of an inflaton $\phi$ coupled
to multiple interacting daughter fields $X_n$ ($n=1,\dots N_d$) through
quadratic-quadratic interactions $g_n^ 2\phi^2 X_n^2$. We assume a monomial
inflaton potential $V(\phi) \propto |\phi|^p$ ($p \geq 2$) around the minimum.
By simulating the system in 2+1-dimensional lattices, we study the
post-inflationary evolution of the energy distribution and equation of state,
from the end of inflation until a stationary regime is achieved. We show that
in this scenario, the energy transferred to the daughter field sector can be
larger than $50\%$, surpassing this way the upper bound found previously for
single daughter field models. In particular, for $p \geq 4$ the energy at very
late times is equally distributed between all fields, and only $100/(N_d + 1)
\%$ of the energy remains in the inflaton. We also consider scenarios in which
the daughter fields have scale-free interactions $\lambda_{nm} X_n^2 X_m^2$,
including the case of quartic daughter field self-interactions (for $n=m$). We
show that these interactions trigger a resonance process during the non-linear
regime, which in the single daughter field case already allows to deplete more
than $50\%$ of the energy from the inflaton for $p\geq 4$.
