  We discuss the $SU(5)$ grand unified extension of flavour models with
multiple modular symmetries. The proposed model involves two modular $S_4$
groups, one acting in the charged fermion sector, associated with a modulus
field value $\tau_T$ with residual $Z_3^T$ symmetry, and one acting in the
right-handed neutrino sector, associated with another modulus field value
$\tau_{SU}$ with residual $Z_2^{SU}$ symmetry. Quark and lepton mass
hierarchies are naturally generated with the help of weightons, which are SM
singlet fields, where their non-zero modular weights play the role of
Froggatt-Nielsen charges. The model predicts TM$_1$ lepton mixing, and
neutrinoless double beta decay at rates close to the sensitivity of current and
future experiments, for both normal and inverted orderings, with suppressed
corrections from charged lepton mixing due to the triangular form of its Yukawa
matrix.
