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We develop a general formalism for multiple moduli and their associatedmodular symmetries. We apply this formalism to an example based on three moduliwith finite modular symmetries $S_4^A$, $S_4^B$ and $S_4^C$, associated withtwo right-handed neutrinos and the charged lepton sector, respectively. Thesymmetry 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 totrimaximal TM$_1$ lepton mixing, consistent with current data, without flavons.

Multiple modular symmetries as the origin of flavour