Murkowski is younger and under more primary pressure, whereas I think Manchin is happy to sail into the sunset in 2024 so party switching would do nothing for him.
I think if Murkowski does leave the Republican party though it will be to sit as an Independent.
Just curious, does Murkowski have to caucus with anyone? Could you have a senate where literally no party had a majority?
Senators are not required to caucus with a party. Dean Barkley during his two months in the Senate in 2002 did not caucus with Democrats nor with Republicans. So that scenario is theoretically possible.
It is theoretically possible, but it's worth noting that it would deprive that senator of committee assignments. I could see a scenario where a senator is kind of a free agent at the start of each Congress, but it seems unlikely anyone would choose to caucus as an independent as anything other than a temporary solution.