It would likely be impossible to nerf ninja for specific mode only.

It is very easy to fix: 3v3 teams should follow the same rule as single lineup does: only one copy of a ninja, with exception of mains. No more 3x Samehada Kisame, 3x Edo Hiruzen, 3x Halloween Kimimaro and so on. Most teams out there are group teams to begin with, so players would be able to decide who takes who.