And framing this as a partisan issue is how you lose. Changes to the voting system that allow multiple parties aren't going to cause Democrats to win more seats in Missouri. Missouri is red regardless of which voting system you use. But it will cause Republicans to lose seats, to libertarians or some other right-leaning third party running candidates there. Which is perfectly to the advantage of the right-leaning voters there, because it better represents their interests.
It's not to the advantage of the incumbent party insiders, who then trick people with crooked amendments like that. But if you pin that generically on "Republicans", implying a contrast with Democrats and need for all right-leaning people to line up against you, you're not going to win in Missouri.
You have to pin it specifically where it belongs, on the fat cats trying to sustain their privileged position as a one-party monopoly in the state at the expense of all voters.