If it works for 1 your algorithm works for any number so far I can follow. It's a bit tricky to show that the 3-way merge always works fine if you've got a sin

If it works for 1 your algorithm works for any number so far I can follow. It's a bit tricky to show that the 3-way merge always works fine if you've got a single least common ancestor. But yeah it looks like you're fine because any update that both have in common will also have reached the LCA (this was the insight I was missing that explains why a single LCA works and multiple LCA do not if you naively apply the 3-way-merge).