I don't know how many (if any) engravers did work for multiple gunmakers, but I suspect some of them probably did.
I know Frank Mason was the primary engraver for Baker Gun & Forging Co. until approximately 1907. He did the engraving on their high grades and maybe worked on some of the A and B grades that were engraved (instead of etched). I've heard that he may have also done work for Lefever Arms in Syracuse as well, but I have my doubts.
Joseph Loy was the engraver for Ithaca on their higher grades. But I've seen other doubles (some Remington 1894) that have very similar dogs, game birds, scroll, etc. and have read that Loy may have worked on these. So maybe some of the better engravers did freelance some with other firms.
I have a feeling that certain patterns and compositions that were very popular were "copied" and the engravers used similar styles and simply put their own spin on things.