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The aim of this paper is to study the stability of solitonlike static solutions via nonlinear simulations in the context of a special class of massive tensor-multiscalar 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 κ = 0 these solutions reduce to the standard boson stars, while for κ ≠ 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 ψc while instability kicks in with the increase of ψc. 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. Moreover, different scenarios for unstable solutions--i.e., collapse or expansion of unstable initial configurations--have been investigated by assuming different perturbations around equilibrium. [ABSTRACT FROM AUTHOR]