  The equation of state (EoS) of asymmetric nuclear matter at high densities is
a key topic for the description of matter inside neutron stars. The
determination of the properties of asymmetric nuclear matter, such as the
symmetry energy ($a_{sym}$) and the slope of the symmetry energy ($L_0$) at
saturation density, has been exaustively studied in order to better constrain
the nuclear matter EoS. However, differently from symmetric matter properties
that are reasonably constrained, the symmetry energy and its slope still large
uncertainties in their experimental values. Regarding this subject, some
studies point towards small values of the slope of the symmetry energy, while
others suggest rather higher values. Such a lack of agreement raised a certain
debate in the scientific community. In this paper, we aim to analyse the role
of these properties on the behavior of asymmetric hyperonic matter. Using the
formalism presented in Ref. (R.O. Gomes et al 2014}, which considers many-body
forces contributions in the meson-baryon coupling, we calculate the EoS of
asymmetric hyperonic matter and apply it to describe hyperonic matter and
hyperon stars.
