Yes, it is possible unfortunately. I have RA and ankylosing spondylitis (also related to HLA B27 gene), RA and PsA/AS are both autoimmune but work through different mechanisms and so different drugs/treatments can work better or worse for the various symptoms. It is great that your doctor recognised this so that your treatment can be tailored. Wishing you the best of luck with it.

It is very possible to have more than one autoimmune disease.

Yes, it is common unfortunately. You'll find that many of us have multiple diagnoses of autoimmune diseases and truly felt the same way as you in the beginning. After 6 years of this new road...I still go through the denial and griefs of accepting what the "quacks" have told me.😉
Keep asking your questions so you can understand better what you are experiencing. (((Hugs)))

Yes I am positive for the rheumatoid factor. I don't have the pitting in my nails but do have a flaking in my ear. Years ago after my first child was born I had terrible scalp problems with whole chunks of scalp coming up. Went to a dermatologist and got meds and it went away for years, but I think that was the start of my psoriasis. It comes and goes the severity. It doesn't matter how many autoimmune diseases you have which I have the
ankylosing spondylitis as well, its the treatments that make it manageable. Just had 2 great months of being free of pain. But with the stress of the hurricane here in Fl I am back to the terrible inflammation with a great deal of pain. But it also will pass. Eating right and exercise helps me the most.

Along with my arthritises I am gluten intolerant and I think that is more on the Psoriatic side.