  We report some results on the quenched disordered Spherical multi-$p$-Spin
Model in presence of ferromagnetic couplings. In particular, we present the
phase diagrams of some representative cases that schematically describe, in the
mean-field approximation, the behavior of most known transitions in glassy
materials, including dynamic arrest in super-cooled liquids,
amorphous-amorphous transitions and spin-glass transitions. A simplified
notation is introduced in order to compute systems properties in terms of an
effective, self-induced, field encoding the whole ferromagnetic information.
