According to the New York Times, McConnell has told Biden that whether such a move is possible must be determined by Senate Parliamentarian Elizabeth MacDonough, the official whose role it is to advise the Senate on such procedural matters. Even if McConnell is on board, the path to a bifurcated schedule isn’t clear. Some have suggested that this move, too, would require another unanimous consent approval, which could prove difficult to obtain.
This sort of procedural talk might make your eyes glaze over, but this question is actually very important. If the parliamentarian rules that the two-track system requires unanimous consent, then any single senator with an axe to grind against the trial would have the ability to gum up all the rest of the Senate’s business in protest against the proceedings. If she rules otherwise, McConnell and Schumer would be able to strike a deal that would lead to an extremely busy February in the Senate—but one that will avoid leaving Biden’s Cabinet nominees congealing on the back burner.