I would not do pets, you may find a good renter and the other may be allergic to cats.

Including people sharing rooms.I personally would like to, at the very least, see ESAs limited to normal domestic pets. 

This is a well qualified tenant who I waived the pet fee and application fee to have move in.After the walk through and after signing the lease agreement and being given the deposit, the tenant has asked for a series of small repairs.

(trashing the property, not changing air filters, overlooking repairs, unauthorized pets)6) What is your process for handling service requests?

The original lease states that no pets are allowed.  

Pets, really consider, if its a pet lovers house, you will get a half a dozen of them in the house with one or 2 pets per room. 

I do allow pets in my places.

If the existing lease does this, then take the time you need to get your own lease docs prepared, then if you like this tenant and the terms, sign a new lease under you or your company.BP has form lease packages for free if you are or become a Pro member, or you can search for a standard lease, lease addendum, pet agreement, etc., on the Internet. 

Besides potential danger to people and pets, you don't want any critters dying in the walls.

Don't wait until they sneak a dog in to learn how to deal with an unauthorized pet.