  A model based on a microscopic Brueckner--Hartree--Fock approach of hyperonic
matter supplemented with additional simple phenomenological density-dependent
contact terms is employed to estimate the effect of hyperonic three-body forces
on the maximum mass of neutron stars. Our results show that although hyperonic
three-body forces can reconcile the maximum mass of hyperonic stars with the
current limit of $1.4-1.5 M_\odot$, they are unable to provide the repulsion
needed to make the maximum mass compatible with the observation of massive
neutron stars, such as the recent measurements of the unusually high masses of
the millisecond pulsars PSR J1614-2230 ($1.97 \pm 0.04 M_\odot$) and PSR
J1903+0327 ($1.667 \pm 0.021 M_\odot$).
