There are about 70,000 students in state universities not part of the University of Missouri system, or about half of the public university students in the state.
The largest is Missouri State, then there are the directionals - Southern, Western, Southeast, Central, Northwest; add in Truman and the two Black schools.
UofM does appear to have a monopoly on doctoral level degrees. But by the time you get to doctoral level studies, you should be able to get the out of state tuition taken care of as part of your package.