Can two bills be set up to be voted on, one immediately after the other... [View all]

[Silent3]

...under either the House or the Senate rules?

If so, I think a great way to handle Republican amendments to any bill, amendments accepted in order to garner Republican support, would be to have a bill to undo all of those amendments ready to go.

If Republicans still vote "no" against the first bill that contains their amendments, then a simply majority of Democrats would immediately pass the second bill that reverses the Republican amendments, producing the result the Democrats wanted in the first place, before that just-proven-to-be-fruitless effort at bipartisanship.