Why not?  It's a perfectly reasonable request.  At the very least, by way of explanation for reasoning, you can explain that you already have one Yorkie and that if you take the second, you would not want both to become ill by something they might not even know about and ask for a health certificate, or their vet's phone number and that they authorize their vet to talk to you, etc.  If you are interested in taking this dog, it is certainly worth it.  If they refuse, maybe it wasn't such a good idea to begin with...sad as that sounds to say.  I find that when things are supposed to work, they do, regardless of what I do...and if not...same thing!  

  It's still so exciting, though...a second Yorkie...maybe!!!
