  We develop a bottom-up approach to flavour models which combine modular
symmetry with orbifold constructions. We first consider a 6d orbifold
$\mathbb{T}^2/\mathbb{Z}_N$, with a single torus defined by one complex
coordinate $z$ and a single modulus field $\tau$, playing the role of a flavon
transforming under a finite modular symmetry. We then consider 10d orbifolds
with three factorizable tori, each defined by one complex coordinate $z_i$ and
involving the three moduli fields $\tau_1, \tau_2, \tau_3$ transforming under
three finite modular groups. Assuming supersymmetry, consistent with the
holomorphicity requirement, we consider all 10d orbifolds of the form
$(\mathbb{T}^2)^3/(\mathbb{Z}_N\times\mathbb{Z}_M)$, and list those which have
fixed values of the moduli fields (up to an integer). The key advantage of such
10d orbifold models over 4d models is that the values of the moduli are not
completely free but are constrained by geometry and symmetry. To illustrate the
approach we discuss a 10d modular seesaw model with $S_4^3$ modular symmetry
based on $(\mathbb{T}^2)^3/(\mathbb{Z}_4\times\mathbb{Z}_2)$ where $\tau_1=i,\
\tau_2=i+2$ are constrained by the orbifold, while $\tau_3=\omega$ is
determined by imposing a further remnant $S_4$ flavour symmetry, leading to a
highly predictive example in the class CSD$(n)$ with $n=1-\sqrt{6}$.
