Penn Station doesn’t have to be a homeless-plagued disaster zone — just look at Grand Central Terminal.

Even before one vagrant’s stabbing rampage a week ago, local leaders shrugged off the issue, but New Yorkers (and New Jerseyans) have every right to ask why the city’s primary train station has to be a living room for mentally ill and homeless people.

A few years ago, the lower-level food court at Grand Central was a mess, with vagrants camping out at tables and washing their socks in the restroom.

Some restaurant owners threatened to withhold rent if management didn’t clean up the venue.

The MTA, which owns GCT, got the message and reorganized the food court; the area is now orderly and respectable (albeit with nowhere to sit).

New York’s laws prevent outright ejection of vagrants from public property, but that’s no excuse.

One key for Grand Central: closing for a few hours every night, a change that allowed management to make everyone leave.

Another: A single authority over the whole property, since the MTA owns the station and runs nearly all the train lines it serves, meaning clear accountability for policing and homeless outreach.

Penn’s managerial structure is almost as complex as its labyrinthine physical layout, which enables people to skulk in remote corridors.

Amtrak owns the station, but the LIRR and New Jersey Transit oversee their concourses; each authority can pass the buck: If everyone’s responsible, nobody’s is.

This mess calls for leadership, something New York and New Jersey politicians plainly can’t manage.

Happily, President Donald Trump has taken control of the planned massive reconstruction of Penn Station.

That work can make at least some interior changes that discourage vagrants from congregating, but it should bring management changes, too.

Put one central authority in charge of policing Penn; figure out how to close all areas for at least an hour or three overnight.

Heck, Mr. President, don’t wait on final rebuild plans to start cracking down: Begin setting Penn Station straight now.