When I was leaving my second comment under a new contributor's post, I got a duplicate message:
User is a new contributor. Be nice, and check out our Code of Conduct.
Sadly, the limit is two, no matter how many further comments you leave. Refreshing the page removes the second notice until you add another comment.
I also think I saw this on an answer where I hadn't previously commented, but I can't seem to reproduce that again.