Sure. If the smaller planet is very dense and the larger planet is not. Mass-wise no. But I don't think that's what you are after.
Check out this page https://en.wikipedia.org/wiki/Barycenter to get a feel for how planets of near the same size (Mass) might interact.
Also... Who isn't comfortable with calling the Moon a moon? The center of mass is well inside the radius of the Earth (from the wiki page the Sun and Jupiter are a binary, but the Earth and Moon are not).