Gender congruence in adjectives is sort of old-hat. However, let's consider a gender congruence that affects the gender of the main noun instead.¹
Let's assume some nouns, such as "looks", "face", "appearance" - nouns that simply have to do with the visuals of a person - and maybe nouns that have to do with the mental facets of a person - "soul", "mind", "mood", etc - change gender whenever they are possessums.
However, in isolation there is a default gender these nouns take. Maybe they're all neuters or something.
This far, the idea isn't particularly complex or anything - and this seems to be a realistic quirk whereby some nouns denoting certain aspects of a person agrees in gender with that person - nothing weird at all.
How about plurals? Here, we can imagine several possible situations.
1. If the language conflates genders in the plural
Maybe this forces coordinations in cases where mixed gender is implied:
their face-masc and face-fem
their face-masc.pl and face-fem.pl
or maybe singulars are used for these nouns - thus making them overspecify gender while underspecifying number.
If one wants to say that someone has multiple faces, maybe using forced discongruence and coordination could be a solution:
he has face-masc.acc and face-fem.acc
he is two-faced
However, this imho sounds like claiming he does drag, and so
he has face-masc.acc and face-masc.acc
seems more like it would imply twofacedness. "He has faces" would sort of be blocked by the congruence rule - although one could imagine that the use of incongruent nouns in this case would convey a rather marked meaning - viz. that of having two (conflicting) faces.
2. If the language distinguishes genders in the plural
Here, we can imagine more combinations: their.fem appearance.sg.fem implies a shared appearance, their.fem appearance.pl.fem implies the appearances of each of them taken as a group. Number discongruence with gender congruence may be used to indicate a variety of things (a person of many faces, or many people of one appearance), and gender discongruence would probably not be used all that much.
Finally, if the nouns normally are neuter, one could imagine that masculine or feminine forms are used as a sort of derivation that implies, say female or male looks, faces, etc in specific without necessarily talking about a specific face.
Finally, a question: can we create a distribution that is "alignment-like" out of this idea?
¹ Yes, I am aware that in some languages, syntactic analysis indicates that the genitive noun is higher up in the syntactic hierarchy, but let's ignore that for now.