re: Is it possible Biden runs some Democrats over to the R side of the aisle?

It is possible.

But the Democrats know power. With them holding the House and the Senate in the balance it would take some arm bending to get one Senator to switch to regain control of the Senate, but I wouldn't expect it.

There have been some in the past that have negotiated power shifts only because the power shifted to the opposing party.

Billy Tauzin was one of them. He was life long Democrat and had gained enough seniority that he was in line to be a committee chairman, but when the House and Senate shifted Republican in 1995 he lost his opportunity to become a committee chairman. He lost that when the Republicans took over, so, he negotiated and got the Republicans to agree to give him his seniority on the committee and he would become the next chairman if he switched. He eventually switched and gave us bad bill after bill. Such as the Telecommunications Act of 1996 and the Medicare Prescription Drug bill that is bankrupting Medicare.

He then took a lofty position as the head of the Pharmaceutical Lobby for a few years. Now I think he lives at his ranch in Texas.