Two planets in HD 3167 system are on perpendicular orbits, astronomers say

Just a little mind game: What would be the result if two stars with planets in different planes of orbit merged?

Would the planets keep orbiting in their original (different) orbital planes? Or would the planes of orbit merge also so that all the planets began revolving in that new orbital plane?

My feeling is that the two original different orbital planes would be retained, with some planets orbiting in one plane, and other planets orbiting in the other plane.