You are correct to point out that the last major shift in party system was 1859 with the emergence of the new Republican Party and the demise of the Whigs.

I do not believe the current GOP will disappear nor do I believe a new party will arise in its place.

In a parliamentary system, if no party gets an outright majority, two or more parties join together in a coalition to reach a majority.

Under our system, both major parties are essentially coalitions. The Democratic coalition goes from the farther left Progressive Caucus to center-left Democrats (the majority) to center-right. The center-right is much smaller, often with politicians from swing or conservative states or districts such as Joe Manchin.

The GOP used to have factions as well. There were the isolationist and fringe factions underpinned by the John Birch society in the 1950s &1960s. The other factions were the more internationalist Republicans mostly from the northeast such as Eisenhower, Rockefellers and Bushs. Then there was the westerners such as Goldwater and Reagan. The downturn of the GOP really took root in 2010 with the rise of the Tea Party. They resurrected the Red Scare tactics with the fight over Obamacare as socialist. The Tea Party laid the groundwork for MAGA which has effectively taken over the party.

Here in Michigan, ostensibly, MAGA got pushed out and the GOP put in place Pete Hoekstra as state party chair- an ostensible mainstream Republican. But it should be remembered that Hoekstra was part of the Tea Party movement and in reality is just not as removed from MAGA as he and the state GOP want to present.

I think the GOP will limp on for at least another election cycle with MAGA dominant. They have too many MAGA in safe Congressional districts to be able to get rid of them