  The aim of this paper is to study the stability of soliton-like static
solutions via non-linear simulations in the context of a special class of
massive tensor-multi-scalar-theories of gravity whose target space metric
admits Killing field(s) with a periodic flow. We focused on the case with two
scalar fields and maximally symmetric target space metric, as the simplest
configuration where solitonic solutions can exist. In the limit of zero
curvature of the target space $\kappa = 0$ these solutions reduce to the
standard boson stars, while for $\kappa \ne 0$ significant deviations can be
observed, both qualitative and quantitative. By evolving these solitonic
solutions in time, we show that they are stable for low values of the central
scalar field $\psi_c$ while instability kicks in with the increase of $\psi_c$.
Specifically, in the stable region, the models oscillate with a characteristic
frequency related to the fundamental mode. Such frequency tends to zero with
the approach of the unstable models and eventually becomes imaginary when the
solitonic solutions lose stability. As expected from the study of the
equilibrium models, the change of stability occurs exactly at the maximum mass
point, which was checked numerically with a very good accuracy.
