Hi @Lynn you might find this thread helpful if you click here
In answer to your question, you can select the categories “all pets”, “no pets” or “search for a particular pet or pets depending on which pets you would like to sit for in the search”.
I suggest if you select the pets you would like to sit for and search and then select the no pets option and search you can also see if there are any sits without pets and choose from there. Just bear in mind there will be less if any sits showing without pets for your particular search.
There isn’t a way to search for particular pets with the no pets option as well. I hope this helps.