  In this work, we study magnetic field effects on neutron star matter
containing the baryon octet and additional heavier spin 3/2 baryons (the
$\Delta$'s). We make use of two different relativistic hadronic models that
contain an additional vector-isovector self interaction for the mesons: one
version of a relativistic mean field (RMF) model and the Chiral Mean Field
(CMF) model. We find that both the additional interaction and a strong magnetic
field enhance the $\Delta$ baryon population in dense matter, while decreasing
the relative density of hyperons. At the same time that the vector-isovector
meson interaction modifies neutron-star masses very little ($<0.1~M_\odot$), it
decreases their radii considerably, allowing both models to be in better
agreement with observations. Together, these features indicate that magnetic
neutron stars are likely to contain $\Delta$ baryons in their interior
