This is the first time I have seen someone with two emotional support dogs. You certainly can ask for an ESA statement from a medical professional though I would look very close at the language to confirm that two animals are necessary. This may be a case where they are calling them ESA when they are not, but you never know.
An legitimate ESA is considered a medical tool in the same way a cane or walker would be. You cannot deny a tenant because of an ESA unless the ESA is too big for a property (such as a horse in an apartment) or unless the property is a small multi-unit and you live there (duplex or 4-plex). You also cannot charge extra rent or security deposit for an ESA.
The tenant is still responsible for any actions the animal takes that are inappropriate. If there is damage done, treat it like the tenant did it. If the animal is disruptive, treat it like the tenant did it. If an offense occurs too often and you determine it is a lease violation, you can take action.
It would be in your best interest to read up on ESA and Service Animals. You don't want to be accused of violating fair housing due to a tenant's 'medical needs'.