We discuss neutron stars with strong magnetic mean fields in the framework of Extended Theories of Gravity .
In particular , we take into account models derived from f ( R ) and f ( \cal G ) extensions of General Relativity where functions of the Ricci curvature invariant R and the Gauss-Bonnet invariant { \cal G } are respectively considered .
Dense matter in magnetic mean field , generated by magnetic properties of particles , is described by assuming a model with three meson fields and baryons octet .
As result , the considerable increasing of maximal mass of neutron stars can be achieved by cubic corrections in f ( R ) gravity .
In principle , massive stars with M > 4 M _ { \odot } can be obtained .
On the other hand , stable stars with high strangeness fraction ( with central densities \rho _ { c } \sim 1.5 - 2.0 GeV/fm ^ { 3 } ) are possible considering quadratic corrections of f ( \cal { G } ) gravity .
The magnetic field strength in the star center is of order 6 - 8 \times 10 ^ { 18 } G. In general , we can say that other branches of massive neutron stars are possible considering the extra pressure contributions coming from gravity extensions .
Such a feature can constitute both a probe for alternative theories and a way out to address anomalous self-gravitating compact systems .