You sure? There are 22 PLL cases with no parity (included the solved case), yes, but that is because there are a lot of identicals theough symmetry thanks to AUF. I'm not entirely sure it's the same with parity.
For example, see "corners only" PLLs: without parity, there are 4 of them (Aa, Ab, E, X), but with parity, there are 5 at least (UFL-UFR swap, UFL-UBR swap, Oa swap, Ob swap, zig-zag)