Rover has a feature for additional dog fee, I am guessing they did that because they seem to think this should be the norm. I discount for the second and any additional dog for the same reason that most other sitters do so: It isn't much more work to care/watch one dog than for two or more dogs that live in the same household. Specially if they are small dogs, friendly dogs or if you have a yard to just take them out at the same time instead of having to leash them one at a time.
I believe that a person shouldn't be punished for having a big heart. I have watched as many as 5 dogs at once from the same customer and it wasn't any more work than watching two (the owners are the ones to watch out for)
I not only lower the first dog rate but depending on how busy I am or how easy the dogs are to watch I lower the first dog too: Instead of doing each dog at $20 as advertised I do 1st dog $15, 2nd dog $10 for a total of $25 for both or 1st dog $15, 2nd dog $10, 3rd $10, 4th $5, 5th $5 for a total of $50 for five dogs.
I'm not in it for the money, but I do make money since I make many loyal customers.
I offer a discount for the family if they have multiple dogs. I just think it's good business practice for me personally. I get regular repeat clients this way. I know the dogs and know what to expect during their stay. It really is your personal preference if you choose to discount the second dog.