We employ classical density-functional theory to investigate the phase diagram of an assembly of mutually penetrable, parallel ellipsoids interacting via the generalized exponential model of index four (GEM-4) pair potential. We show that the crystal phases of the system are obtained from those of the spherically symmetric GEM-4 model by rescaling the lattice vectors. Performing this rescaling in combination with an arbitrary rotation of the lattice leads to infinitely many different structures with the same free energy, thereby implying their infinite degeneracy. These findings generalize to non-zero temperature the results formerly obtained by us [Pini et al., J. Chem. Phys. 153, 164901 (2020)] for the ground state of a similar system of ellipsoids interacting via a Gaussian potential. According to the mean-field free-energy functional used here, our conclusions apply to soft-core potentials both when they form cluster crystals as the GEM-4 and when they form single-occupancy crystals as the Gaussian itself.
