By the way, if there is any way you can just rent to grad students - preferably med students or law students or engineering students - just not art or theater majors (party animals!)

(2) Does the person making the request have a disability-related need for an assistance animal?

If a tenant has an emotional support animal or service animal, none of the "pet" language applies, though.You should create an Animal Addendum, or Animal Clause, that applies to all animals, whether they are pets or not. 

If you do allow it, just be sure to explicitly state on the lease and explain verbally that they are allowed "2 Guinea Pigs" only and that any other animals are prohibited without your prior written consent.

I know this insurance stuff is hard, but basically just remember, for property coverage animals are never ever ever ever covered, ever.

While I sympathize with the plight of the animal the owner who left the animal behind should be prosecuted. 

In your case, I would justify the intra-lease charge by pointing to the impaired usage of the property for the other tenants and the pet addendum terms calling for immediate cleanup of animal waste.  

If the animal causes damages, you can charge the tenant for those damages.Best to establish a Service Animal/Assistance Animal policy proactively.

@Demetri T.I'm no lawyer like you are, but I don't think "companion animals" get the same protections as service animals.

Pets are animals not human family members and should never take priory when making real life decisions.