Need help fixing formula (single value for multiple selections)

I was working on coming up with a formula that if the user selects either one choice or multiple choices in the same category it will equal the same or highest amount. The sample data I used was as follows:

Dog, cat = 3

Mouse, rat = 2

Snake, lizard = 1

The following formula was suggested to me and it does work to a certain degree:

=IF(OR(HAS([Animal dropdown]@row, "Dog"), HAS([Animal dropdown]@row, "Cat")), 3, IF(OR(HAS([Animal dropdown]@row, "Mouse"), HAS([Animal dropdown]@row, "Rat")), 2, IF(OR(HAS([Animal dropdown]@row, "Snake"), HAS([Animal dropdown]@row, "Lizard")), 1)))

The problem I'm having is when multiple selections are made. If two selections are made, even with the same value, the cell goes blank. Instead of selecting dog and cat = 3 or dog and mouse = 3 the cell won't give a value. However, if a single selection is made it will give it the corresponding value such as selecting snake = 1. I've tried different ways but I can't get it to work. Any suggestions would `be greatly appreciated.