Assuming Biden wins but does not have a majority in the senate, could Biden appoint Mitch McConnell as say, the Secretary of Veterans Affairs, in order to remove him from his position as Senate Majority Leader? Of course, McConnell would be replaced by another Republican senator via appointment, but with him gone, the next Senate Majority Leader might be slightly more willing to negotiate and to allow bills that pass the House to be debated. Especially if some of the more moderate Republicans such as Collins or Murkowski vote across party lines, some pieces of relatively uncontroversial legislation such as infrastructure bills and whatnot might actually get passed this way. So would this be a plausible strategy?
Biden could suggest that deal, but McConnell would be free to reject it.
The President can fire his cabinet members at will, and should he or she decide to do that with an ex-representative, that representative would not get their job in congress back. So it's a deal Biden would have to sweeten a lot for McConnell to seriously consider it.