Or, rather than declaring a Consensus Party outright, what about this idea...

At the beginning of a new congressional session: a critical mass of conservative-to-moderate Democrats and liberal-to-moderate Republicans could jointly switch their individual party affiliations to "I" -- and then, like a union, they'd "threaten" to caucus with whichever major party offers them the best deal in terms of negotiation and leverage.

An example: what if, in January 2023, no matter which party is supposed to be controlling the U.S. Senate, going in -- Joe Manchin, Kyrsten Sinema, Susan Collins, and Lisa Murkowski all jointly change their party affiliations to "I" (rather than "D" or "R"). As a unit, essentially a group of "unionized centrists." Hell, throw in Jon Tester and Dr. Oz (if he defeats Fetterman in Pennsylvania), just for good measure.

McConnell and Schumer would then be forced to separately court all 4-6 of them, as a unit, to caucus with his party to maintain his goal of being Majority Leader.

I personally don't like either McConnell or Schumer -- but wanna guess who would make them the better deal?

The risk for the partisan die-hards would be, at any moment, any combination of them could "flip back" and obliterate the majority party's leverage and/or controlling status.

House Democrats/Republicans could do something similar to Pelosi and McCarthy, over in the House.