  We compute the parametrized post-Newtonian parameter $\gamma$ in the case of
a static point source for multiscalar-tensor gravity with completely general
nonderivative couplings and potential in the Jordan frame. Similarly to the
single massive field case $\gamma$ depends exponentially on the distance from
the source and is determined by the length of a vector of non-minimal coupling
in the space of scalar fields and its orientation relative to the mass
eigenvectors. Using data from the Cassini tracking experiment, we estimate
bounds on a general theory with two scalar fields. Our formalism can be
utilized for a wide range of models, which we illustrate by applying it to
nonminimally coupled Higgs SU(2) doublet, general hybrid metric-Palatini
gravity, linear ($\Box^{-1}$) and quadratic ($\Box^{-2}$) nonlocal gravity.
