Some statehouses try bipartisanship. It’s been a rough start.

As Republicans in the nation’s capital were grinding through 15 ballots to elect California Rep. Kevin McCarthy speaker of the House, some states have been navigating their own razor-thin legislative majorities and intraparty divides in a different way – by reaching across the aisle. 

This month, 16 Pennsylvania House Republicans, including all seven GOP leaders, unexpectedly joined with Democrats to elect Democrat Mark Rozzi as speaker. Ohio also saw a surprise candidate elected speaker of the House – a Republican who won by drawing votes from both parties. And Republicans and Democrats in Alaska’s narrowly divided state Senate have agreed to form a bipartisan coalition.

It’s an alternative model for parties grappling with extreme wings: Instead of trying to hold an unmanageable caucus together, create a bipartisan governing majority. Whether the approach is workable in an age of hyperpolarization, however, remains to be seen. Already, the path in Pennsylvania has been anything but smooth.  

In battleground states, where the stakes are so high, it’s especially difficult for the two sides to trust each other, says Dan Mallinson, a public policy professor at Penn State Harrisburg. “It’s not that it’s impossible,” he says. “But it’s increasingly hard.”  

As state Rep. Jim Gregory walks into the Pennsylvania Capitol’s cafeteria, a table of Democrats all stops talking and turns their heads. One stands up to give him a pat on the back as he passes by.

Mr. Gregory, a Republican, ruefully remarks that this reception was likely warmer than what he’d be getting from Republicans in his home district. He’s not wrong.

A few weeks ago, Mr. Gregory did something that made him unpopular with members of his own party: He nominated a Democrat to be speaker of the Pennsylvania House.

As Mr. Gregory saw it, his action was a reasonable response to a unique and difficult set of circumstances. In November, Democrats won a majority in the Pennsylvania House for the first time in more than a decade, by a single seat. But three Democratic-held seats then immediately became vacant (one candidate died right before Election Day and two others resigned after winning higher office) – leading to heated debates about which party really held the majority, and who should become speaker.

Searching for a solution, Mr. Gregory, who represents a district in central Pennsylvania surrounding Altoona, started floating the possibility of nominating Berks County Democrat Mark Rozzi.