Maybe one way of doing it would be to have multiple select by attribute tools each selecting by month. That would select the polygons for a single month but for all years. After that you can run the intersect tool on the feature class itself (input the same feature class twice for the intersect tool). This assumes that each feature class contains information for a single animal. If not, you should create a selection on the animal first, then create month attribute selections from the existing animal selection.
Another way of doing this might be using a python script if you are familiar with python. It would allow you to easily iterate over your data which Model builder allows you to do but has a limit of one iteration tool per model.
I hope that helps!
Hi Kevin, thank you for taking time to respond. I am not sure I follow you as I still don't see a way to do a month by month comparison to calculate percentage overlap. Thanks anyway, and unfortunately, I have never used python so that may not be an option at this time.