  The field equations for static EGBM gravity are obtained and transformed to
an equivalent form through a coordinate redefinition. A form for one of the
metric potentials that generalises the spheroidal ansatz of Vaidya--Tikekar
superdense stars and additionally prescribing the electric field intensity
yields viable solutions. Some special cases of the general solution are
considered and analogous classes in the Einstein framework are studied. In
particular the Finch--Skea ansatz is examined in detail and found to satisfy
the elementary physical requirements. These include positivity of pressure and
density, the existence of a pressure free hypersurface marking the boundary,
continuity with the exterior metric, a subluminal sound speed as well as the
energy conditions. Moreover, the solution possesses no coordinate
singularities. It is found that the impact of the Gauss--Bonnet term is to
correct undesirable features in the pressure profile and sound speed index when
compared to the equivalent Einstein gravity model. Furthermore graphical
analyses suggest that higher densities are achievable for the same radial
values when compared to the 5--dimensional Einstein case. The case of a
constant gravitational potential, isothermal distribution as well as an
incompressible fluid are studied. All exact solutions derived exhibit an
equation of state explicitly.
