In our Gemeinde in SZ there is a base rate for the first dog. Then the total number of dogs in the household is used as a multiplier to determine the final amount.
(Farm dogs are a flat, much reduced rate.)
I have three, so my tax is usually somewhere between CHF 450 and 600.
The amount seems to vary, I have never been able to figure out why. But as the owner of more dogs than is deemed culturally acceptable here I frankly don't want to poke that particular hornet's nest by pushing for an explanation.
I just pay whatever they ask.