You’re assuming the democrats and this new party would vote the same for SotH and all important bills, in which case what’s the point of this new party? Also most states use FPTP for congressional elections as well, so while democrats and this third party would likely still win some seats, in most locations they would again split the vote and you’d end up with even more GOP congressional representatives than you have now. So it wouldn’t be 45/35/20 GOP/dem/X, it would be more like 80/15/5. That’s just the nature of how FPTP works.
You’re assuming the democrats and this new party would vote the same for SotH and all important bills, in which case what’s the point of this new party? Also most states use FPTP for congressional elections as well, so while democrats and this third party would likely still win some seats, in most locations they would again split the vote and you’d end up with even more GOP congressional representatives than you have now. So it wouldn’t be 45/35/20 GOP/dem/X, it would be more like 80/15/5. That’s just the nature of how FPTP works.