While in the real world the moon is only really ever full for a single night, in a setting with a moon that has a really long cycle it would be possible for a moon to be full/new/etc. for more than a single calendar day. For example, I have a moon in my setting with a 200 day phase cycle. It would reasonably be full for more than a single night.
I have no idea how you'd actually implement this, I don't know the orbital mechanics well enough to know if there's a way to calculate this. Could possibly just add a "phase length" input somewhere in the moons configuration.