  Guided by old results on simple mode-coupling models displaying glass-glass
transitions, we demonstrate, through a crude analysis of the solution with one
step of replica symmetry breaking (1RSB) derived by Crisanti and Leuzzi for the
spherical $s+p$ mean-field spin glass [Phys. Rev. B 73, 014412 (2006)], that
the phase behavior of these systems is not yet fully understood when $s$ and
$p$ are well separated. First, there seems to be a possibility of glass-glass
transition scenarios in these systems. Second, we find clear indications that
the 1RSB solution cannot be correct in the full glassy phase. Therefore, while
the proposed analysis is clearly naive and probably inexact, it definitely
calls for a reassessment of the physics of these systems, with the promise of
potentially interesting new developments in the theory of disordered and
complex systems.
