  Gravitational theories with multiple scalar fields coupled to the metric and
each other --- a natural extension of the well studied single-scalar-tensor
theories --- are interesting phenomenological frameworks to describe deviations
from general relativity in the strong-field regime. In these theories, the
$N$-tuple of scalar fields takes values in a coordinate patch of an
$N$-dimensional Riemannian target-space manifold whose properties are poorly
constrained by weak-field observations. Here we introduce for simplicity a
non-trivial model with two scalar fields and a maximally symmetric target-space
manifold. Within this model we present a preliminary investigation of
spontaneous scalarization for relativistic, perfect fluid stellar models in
spherical symmetry. We find that the scalarization threshold is determined by
the eigenvalues of a symmetric scalar-matter coupling matrix, and that the
properties of strongly scalarized stellar configurations additionally depend on
the target-space curvature radius. In preparation for numerical relativity
simulations, we also write down the $3+1$ decomposition of the field equations
for generic tensor-multi-scalar theories.
