New Jersey Gov. Phil Murphy, a Democrat, signed a law this month clarifying that a candidate for one of the state’s U.S. Senate or House seats can also run in presidential primaries.

Locals nicknamed it Cory’s Law, a cheeky acknowledgment that Sen. Cory Booker is up for re-election in 2020 and is also expected to launch a bid for the Democratic presidential nomination.

Booker is not the only possible 2020 contender who could benefit from such a change. Oregon’s Jeff Merkley, another Senate Democrat up for re-election next cycle and potentially eyeing a presidential bid, has reportedly asked allies in the Oregon Legislature to tweak the laws there. House members from California, Hawaii, Massachusetts and Ohio would face similar challenges, as would Washington’s governor.

“There are very legitimate reasons to prohibit people from running for two offices,” said James A. Gardner, an expert in election law at the University of Buffalo School of Law. “It does not necessarily speak to the great commitment of the candidate to any particular constituency.”

But there are countervailing reasons to allow exceptions for president, which is relatively common, he added.

“Given, up until recently anyway, the view that the pool of highly qualified presidential candidates is limited, there’s a good argument for not artificially constricting the pool and particularly for not punishing the voters for elevating a talented person,” Gardner said.

Booker wouldn’t be the first senator to seek that privilege.

Joseph I. Lieberman, who ran in 2000 both for re-election to the Senate and as the Democratic candidate for vice president, “took a lot of flak” for running for both offices, Gardner said. Regardless, Connecticut voters sent him back to the Senate that year when his running mate, Vice President Al Gore, lost the presidential election. Voters in Delaware and Wisconsin also elected Sen. Joseph R. Biden Jr. in 2008 and Rep. Paul D. Ryan in 2012 to their congressional posts despite both running concurrently for vice president.

New York’s Kirsten Gillibrand, Minnesota’s Amy Klobuchar, Vermont independent Bernie Sanders and Ohio’s Sherrod Brown are among those who could focus entirely on a presidential run, if they choose, after decisively winning new six-year terms Nov. 6. California’s Kamala Harris, another potential first-tier contender, won a six-year term in 2016 and would be similarly free to focus on a presidential campaign.

Presidential aspirants seeking to keep their current offices as a fallback option may run some risk of alienating constituents, said Alex Conant, a partner with Firehouse Strategies and communications director for Florida GOP Sen. Marco Rubio’s 2016 presidential bid.

Downsides

“In general, voters want their politicians focused on serving them, not higher office,” Conant said.

Conant also worked for then-Minnesota Gov. Tim Pawlenty, whose home-state support dipped once he began testing the waters for a presidential run, he said. In Rubio’s case, running statewide in a large, competitive state like Florida is all-consuming and can’t be juggled with a presidential campaign, he added.

However, the move could be feasible for someone in a less competitive state or district with “a very stable political support network” back home, Conant said.

That could apply to someone like Booker, who remains quite popular in New Jersey. Ruth Mandel, the director of the Eagleton Institute of Politics at Rutgers, the state university of New Jersey, said she’s observed that the positioning he’s done in anticipation of a presidential race hasn’t appeared to hurt his popularity in the Garden State, especially among young people.

Republicans in the state criticized the Democrat-controlled Legislature’s move to tweak election law for Booker’s benefit, but among those inclined to support him the increased visibility has been positive, Mandel said.

“I don’t believe that any of these people would have any problem voting him on to his Senate seat … while he’s making a presidential run,” she said.

Here are some states where this issue of dual candidacies might pop up in 2020 and an explanation of the laws.

Allowed: New Jersey, Massachusetts, Ohio, West Virginia, Hawaii

No other state went as far this year as New Jersey in explicitly declaring the move legal. But in Massachusetts, where Rep. Seth Moulton has said he’s considering a presidential bid, and Ohio, where Rep. Tim Ryan is reportedly doing the same, the law is fairly clear that candidates can pursue the presidency and another office.

Massachusetts allows candidates to run for different offices in the same year in the general election, but not in the primary. Luckily for Moulton, the presidential primary is in March, and primaries for other offices, including the House, are in September.

In Ohio, the law has several prohibitions against running for two offices at once, but only at the state and local levels. For example, a candidate can’t run for a state office and a federal office or for two state offices simultaneously, but nothing specifically bars a candidate from seeking two federal offices like U.S. House and president.

Asked if either would pursue a clarifying state law in the New Jersey mold, spokesmen for Ryan and Moulton said they didn’t know what the current laws were and declined to comment further.

Hawaii, where Rep. Tulsi Gabbard is reportedly considering a run for president, is among several states that allow carve-outs for would-be presidents or vice presidents but otherwise prohibit running simultaneously for more than one office. Those exceptions are often called LBJ laws after the normally restrictive Texas changed its laws in 1959 to allow Lyndon B. Johnson to seek both the vice presidency and re-election to his Senate seat.

West Virginiaalso falls in that category. State Sen. Richard Ojeda is one of only two declared presidential candidates.

Probably allowed: California

Between trips to the first-in-the-nation caucus state of Iowa, California’s Rep. Eric Swalwell has said he’s considering a run for the White House. The Golden State’s election laws probably permit him to pursue his House seat as well.

State law prohibiting most dual candidacies doesn’t apply to presidential primaries. Plus, the law technically only prohibits filing for two offices, not actually running for them, and candidates for president and vice president do not have to file nominating papers, according to a 2014 document from the National Conference of State Legislatures.

“As is often the case in California, there’s no simple answer,” the document reads.

Not (yet) allowed: Oregon, Washington

Local media have reported that Merkley, the former speaker of the Oregon House, is trying to push for a change to allow him to run for re-election and the presidential nomination in 2020. For now, though, the law is clear: Candidates in Oregon cannot pursue two offices that pay a salary beyond expenses.

The same is true in Oregon’s neighbor, Washington state, where Gov. Jay Inslee will have to decide between running for a third term or for president.

Like Moulton in Massachusetts, Inslee could be helped by the filing calendar. If he runs for president but falters in the early nominating states, he could still withdraw from that race before the filing window for gubernatorial candidates even starts in May.