By chance, have you seen a rheumatologist? I got diagnosed with spondylitis first and Crohn's second, so I took the rheumatologist > gastroenterologist path, and a rheumatologist sort of does what you describe about systemic immune monitoring.
Not perfectly, to be fair. And rheumatology is a criminally overlooked and understaffed specialty. But my rheumatologist has been really good at helping me tie together various issues that seemed unrelated but actually shared a root cause. And, immune problems being what they are, I'd wager most of his patients are in a similar boat, so the whole "let's figure out why your guts are bad AND your joints hurt AND your skin is awful AND... etc" thing is business as usual on his end.