I initially wanted to create a culture that used tides to tell the seasons, I'm sure I still can, but a question on here (I can no longer find it) made me wonder if I could set up a world where one of the moons was much brighter on a few days of the year (once, twice, three times etc, but not 'monthly' or weekly).
I'd want a world roughly the size of earth, and between 1 and 3 moons if possible. I'd like the moon that gets unusually bright to be roughly (0.8 - 1.2 times) the size of our moon. I don't want any 'unnatural' circumstances (like one side of the moon is covered in mirrors). The brightness should be ~the same as our moon for the majority of the time, and then bright for a few days at most when it does become brighter (at least 2-5 times brighter).
I've read A brighter moon that's harder to see but I can't see how to adapt any of those answers.
Is this possible with just multiple moons and orbits?