Harvard could boot individual students too for off-campus conduct if it wanted. Princeton threatens any first-year student who tries to join a Greek organization or any other student who tries to "solicit" them with suspension. Relevant quote from
here:
Any violation of this policy will be regarded as a serious matter. A student who engages in solicitation, as defined above, should expect to be suspended. A freshman who joins, pledges, or rushes a fraternity or sorority should expect to be suspended. A freshman who attends or participates in any other activity or event sponsored by a fraternity or sorority may be subject to a lesser penalty (e.g., disciplinary probation). All relevant facts and circumstances will be taken into account in determining the appropriate penalty.
There's precedent for Ivy League institutions to restrict student behavior this much. They're not on par with the wackadoodle religious schools that have staff members policing the bars near campus to catch students drinking alcohol (looking at you, Liberty University), but they're on the same track.
