I can't say with 100% certainty, but I'm about 99.9999% sure that some are licensed in both Missouri and Illinois.
That's not uncommon in any locale close to state borders. Here in Northern Virginia, plenty of Realtors are licensed in Maryland, and visa versa. As well as in D.C.
I don't know what sort of reciprocity--if any--exists between Missouri and Illinois. You'd have to look into that. Worst case scenario: You'd have to take the same courses twice. Best case scenario: One state recognizes the courses you've taken in another, and you might just have to take the licensing exam. But that would be easy enough to determine.
My advice: Get licensed in both. It'll give you a lot more flexibility and coverage.