  We study relativistic mean-field (RMF) models including nucleons interacting
with scalar, vector and iso-vector mean fields and self- and cross- mean-field
interaction terms. Usually, in such a models the magnitude of the scalar field
increases monotonically with the nucleon density, and the nucleon effective
mass decreases. We demonstrate that the latter quantity stops to decrease and
the equation of state stiffens, provided the mean-field self-interaction
potential rises sharply in a narrow vicinity of the values of mean fields
corresponding to nucleon densities $n> n_{*}>n_0$, where $n_0$ is the nuclear
saturation density. As the result the limiting neutron star mass increases.
This procedure offers a simple way to stiffen the equation of state at
densities above $n_{*}$ without altering it at densities $n\le n_{0}$. The
developed scheme allows an application to neutron stars of the RMF models,
which are well fitted to finite nuclei but do not fulfill the experimental
constraint on the limiting neutron star mass. The exemplary application of the
method to the well-known FSUGold model allows us to increase the limiting
neutron star mass from $1.72~M_\odot$ to $M \geq 2.01~M_\odot$.
