Is it valid to calculate Berry phase when there is energy level crossing?

In case of degeneracy, one has to approach to the problem in a different way. I find some useful references. These might be useful in the case you are considering. Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010), Sec. 2, Phys. Rev. Lett. 52, 2111 (1984), Phys. Rev. B 72, 085110 (2005). I myself have never performed such calculations. My guess is that at the degeneracy point, the Berry phase is not uniquely defined as there are two directions at the that point.