Depends on exactly how you are defining a case. If you are talking about EPLL as the first step of a 2-look PLL system, there are only 3 cases.
If you are talking about pure EPLL (where the corners are already solved and should remain so),
there are more than 12.
Kinda like how on a 3x3, if you are doing EPLL as the first step of 2-look PLL, there are only 2 non-solved cases, but if you consider pure EPLL, there are 4 (ignoring AUFs).