  We prove that the PPT$^2$ conjecture holds for linear maps between matrix
algebras which are covariant under the action of the diagonal unitary group.
Many salient examples, like the Choi-type maps, depolarizing maps, dephasing
maps, amplitude damping maps, and mixtures thereof, lie in this class. Our
proof relies on a generalization of the matrix-theoretic notion of factor width
for pairwise completely positive matrices, and a complete characterization in
the case of factor width two.
