Robert's Rules of Order have a "motion to split" or "division of the question". The UK parliament has a similar rule. It's used for things like this.
The problem is that it makes compromises harder. It's common to say, "I am OK with your motion but it does X harm to my constituents. If you add Y to the bill I'll vote for it." That's a pretty reasonable and common way to reach a compromise, and it doesn't work if other people start splitting the question.
Adding more parties wouldn't really help. The bill still needs 50%+1 to pass. You can do that with one party, or you can assemble a coalition. But either way they're going to make compromises, and splitting a bill makes compromises harder. So US legislatures usually don't have a motion to split.
Still, the UK manages. And so do all of the organizations operating under Robert's Rules. So perhaps it would work.
The problem is that it makes compromises harder. It's common to say, "I am OK with your motion but it does X harm to my constituents. If you add Y to the bill I'll vote for it." That's a pretty reasonable and common way to reach a compromise, and it doesn't work if other people start splitting the question.
Adding more parties wouldn't really help. The bill still needs 50%+1 to pass. You can do that with one party, or you can assemble a coalition. But either way they're going to make compromises, and splitting a bill makes compromises harder. So US legislatures usually don't have a motion to split.
Still, the UK manages. And so do all of the organizations operating under Robert's Rules. So perhaps it would work.