  In a class of modular-invariant models with multiple moduli fields, the
viable lepton flavour mixing pattern can be realised if the values of moduli
are selected to be at the fixed points. In this paper, we investigate a modulus
stabilisation mechanism in the multiple-modulus framework which is capable of
providing de Sitter (dS) global minima precisely at the fixed points $\tau =
{\rm i}$ and $\omega$, by taking into consideration non-perturbative effects on
the superpotential and the dilaton K\"ahler potential. Due to the existence of
additional K\"ahler moduli, more possible vacua can occur, and the dS vacua
could be in general the deepest. We classify different choices of vacua, and
discuss their phenomenological implications for lepton masses and flavour
mixing.
