Overflow if carry out and carry in are both 1?

Question

I am confused because the definitions of overflow I see say we get overflow when carry in and carry out differ. But what if we add two negative numbers such that carry out for the MSB is 1 (meaning that the number extends past the number of bits we have to represent it) but carry in is also 1? Technically the number would still be negative, but overflow would have occurred, right? I think adding 1100 to itself works as an example since 1100+1100=1000 which is not correct algebraically but would still pass the overflow "test"?