  We develop a general formalism for multiple moduli and their associated
modular symmetries. We apply this formalism to an example based on three moduli
with finite modular symmetries $S_4^A$, $S_4^B$ and $S_4^C$, associated with
two right-handed neutrinos and the charged lepton sector, respectively. The
symmetry is broken by two bi-triplet scalars to the diagonal $S_4$ subgroup.
The low energy effective theory involves the three independent moduli fields
$\tau_A$, $\tau_B$ and $\tau_C$, which preserve the residual modular subgroups
$Z_3^A$, $Z_2^B$ and $Z_3^C$, in their respective sectors, leading to
trimaximal TM$_1$ lepton mixing, consistent with current data, without flavons.
