Dog appears to have mange, how to proceed??

Sorry to hear you are having problems. The mites can be passed from one dog to another, but in dogs with healthy immune systems, this doesn't pose a problem, so it's considered non-contagious. But if it were me I would isolate the suspected pup if possible.

I would also call Rover Support and notify them of a potential sick dog in your care - this is to cover you. Best of luck Walt

i would be concerned about sarcoptic mange, which is transmittable to other animals as well as humans. On the other hand it could aslo be demodectic mange which is not transmittable. I have owned several dogs with demodex, it is something they are born with, they can be symptom free (no hair loss) and then something stresses them out and BOOM--hair loss and scratching. My current dog is highly allergic to grass and pollen and exhibits the same symptoms you are describing. I personally would flat out ask what is going on, considering you have other animals. I hope it is anything but sarcoptic mange. I would certainly not let him in contact with other animals, no sharing toys, beds,bowls. And wear gloves or handle as little as possible and wash wash wash your hands. At least until you find out what the problem is. I am sorry you have to deal with that.

Quarantine!! Don't let him touch you or your pets or anything in your house (that's avoidable), and I would begin washing every square inch. It's too cold for him to be outside, so you'll have to crate him to keep him from physical contact. Some mange is not contagious, but some is, and you don't need to take that kind of chance.

Keep him comfortable, but don't touch him, and wash everywhere he has been.