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Guided by old results on simple mode-coupling models displaying glass-glasstransitions, we demonstrate, through a crude analysis of the solution with onestep of replica symmetry breaking (1RSB) derived by Crisanti and Leuzzi for thespherical $s+p$ mean-field spin glass [Phys. Rev. B 73, 014412 (2006)], thatthe 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-glasstransition scenarios in these systems. Second, we find clear indications thatthe 1RSB solution cannot be correct in the full glassy phase. Therefore, whilethe proposed analysis is clearly naive and probably inexact, it definitelycalls for a reassessment of the physics of these systems, with the promise ofpotentially interesting new developments in the theory of disordered andcomplex systems.

Comment on ``Spherical 2 + p spin-glass model: An analytically solvable model with a glass-to-glass transition''