SW, I've just seen a lot of these cases on the tick list - mostly tick diseases, some cancers, some autoimmune in the mixed, and some with all three.
In "the real world", I'm actually a mathematics professor, so I'm constantly evaluating the odds and tendency and the logic of treatment. For example, how long has your dog been on immune suppressants primarily, what has gotten better, what hasn't?
I also have dogs which have complicated medical issues, where things don't show up on tests well. I actually think we have strains in California that they don't have the right tests for.
My Max has a history of perianal fistulas (mostly seen in GSDs). Treatment for that is pred, cyclosporin, or Imuran, so I am familiar with those meds. On the PF list, those are predominantly the meds that dogs respond to. They made it worse for Max. I stopped all the regular meds, and put him on a doxycycline/niacinamide protocol and he started getting better. I searched the blog of a lyme MD and found a multi-antibiotic protocol that he uses for coinfections, and I put my dog on a protocol to mimic that. It took a combination of three different antibiotics to get him better and healed up. In some sense, it flies in the face of common sense and everything conventional. (Btw, I was working with a dermatologist through this, but I started the drug regimines on my own.) Oddly, I am in an area where they say that we don't really have tick diseases.
And the bottom line, is that it might not be a tick disease, for either your dog or mine. But if there is a lack of satisfactory response to the current treatment, and a high likelihood that there is another treatment to try that will not make things worse, then you gotta go in that direction.
Seems to me that pure autoimmune has been ruled out, and you are down to cancer and/or infection, neither of which respond favorably to immune suppression (though a few cancers do seem to respond to pred, which doesn't seem to be happening here).
Have you tried different types of proteins when feeding?
I'm a big fan of vanilla or unflavored whey protein (with no artificial sweeteners), mixed in a favorite liquid. For my girl, it used to be apple juice (and the natural sugars are good when they are not eating). For Max, he loves the green barley drinks, but will also drink the apple juice. The whey protein gives them lots of nutrients, and it's also a cancer fighter.
Did you see anyt of the digestive stuff get better with the decrease in doxy? If not, you might have to add some probiotics, or anti-acids, or l-glutamine for the stomach to tolerate it. All these drugs are hard on the body - all of them.
When Max was on cyclosporine for his fistula, similar to Imuran, I did stop it completely at once, though he was not on it long. He felt a little bit better each day, but it took about a couple of weeks for the antibiotics to start undoing the damage that was done by the suppression.
Do you know which white blood cells are increasing? Neutrophils? Bands? Monocytes? etc?