Mat, I know about complement proteins C3 and C4 in a research but not clinical context.

They are both on the list of acute-phase response proteins, same as CRP - proteins whose levels are elevated in an acute or chronic infection.

Often a chronic infection has an inflammatory aspect so maybe the possible inflammatory aspect (not the same as an infection) of your primary Sjogren's might explain your elevated C3 and C4 levels - your CRP level is also high(?).

This fits with the inflammatory aspect of OA - C3 and C4 could be elevated in it but PubMed does not shed any light on this.