Any exceptions to either it's "A" or "not A"?

After Schrödinger’s Cat, to me the best example of what the OP is after is compatibilism. This is a construct in the free will vs. determinism debate. Normally, the two are considered A vs. not-A, i.e., we have free will or we don’t. Compatibists argue it’s both at the same time. FWIW, I’m a compatibilist, but of an unconventional stripe.