I have an immune deficiency, to put it very simply I don't make antibodies well. This also means I don't respond well to vaccines, part of my diagnosis involved a vaccine challenge, they tested my antibodies to pneumonia, gave me the shot, and tested them again a few weeks later. I didn't gain any immunity.
I'm supposed to get all "dead" vaccines (ex. flu shot, pneumonia) even though they probably won't help me. I'm not supposed to get live vaccines (ex. MMR, chicken pox, nasal flu spray) because I could get sick from them. I have had the MMR and chicken pox shots as a baby/kid without getting sick.
Most dog shots are live vaccines (except rabies).
DVMvac.org | Killed vs. Modified-Live Vaccines
I don't know what I'd do with Mack beyond titer testing and talking to the vet.
If his titers are much lower than expected I may assume he didn't respond to them in the first place (like me) and not vaccinate him.
If he's due for rabies you could do your own vaccine challenge on him, if he doesn't respond I probably wouldn't do the other vaccines.
If his titers are normal low or he responds to the rabies shot I'd probably take the chance and do the other vaccines.