  In this work, we study in detail the effects of many-body forces on the
equation of state and the structure of magnetic neutron stars. The stellar
matter is described within a relativistic mean field formalism that takes into
account many-body forces by means of a non-linear meson field dependence on the
nuclear interaction coupling constants. We assume that matter is at zero
temperature, charge neutral, in beta-equilibrium, and populated by the baryon
octet, electrons, and muons. In order to study the effects of different degrees
of stiffness in the equation of state, we explore the parameter space of the
model, which reproduces nuclear matter properties at saturation, as well as
massive neutron stars. Magnetic field effects are introduced both in the
equation of state and in the macroscopic structure of stars by the
self-consistent solution of the Einstein-Maxwell equations. In addition,
effects of poloidal magnetic fields on the global properties of stars, as well
as density and magnetic field profiles are investigated. We find that not only
different macroscopic magnetic field distributions, but also different
parameterizations of the model for a fixed magnetic field distribution impact
the gravitational mass, deformation and internal density profiles of stars.
Finally, we also show that strong magnetic fields affect significantly the
particle populations of stars
