Consider a typical IE-style gender-case fusional system. In such a system, individual words could be exceptional and behave as members of one gender with regards to some forms, but another with regards to other forms. This might lead to any number of interesting consequences down the line.
In many languages, the case system is inconsistent between genders: different genders or numbers may conflate some cases; alternatively we can think of this as one gender distinguishing more cases than another. Sometimes, however, multiple genders overlap in such a way that over some 'area' of the case system, no particular gender has more case distinctions than another, they just split the case system in different ways, e.g.
|gender 1||gender 2||gender 3|
Here, we have a clear three-case system, with only two distinctions ever made. In fact, even if we eliminated one of the genders from this system, there'd imho be a sufficient reason to consider there to be three underlying cases in this language.
Now, a noun could exceptionally manage to behave like gender 1 with regards to case 1, like gender 2 with regards to case 2, and like gender 1 with regards to case 3. Maybe there's a whole slew of cases where it behaves exceptionally. Maybe it's only a certain combination of number and case that triggers the exception.
However, let's consider a different part of this: pronouns. Consider a language that has different roots for different gender referents. Potentially, we could have, say, gender 1 roots taking gender 2 morphology with nouns like these (or vice versa).