While not a long range missile, stingers are sort of two-stage. They have a launch motor to get the missile clear of the tube & operator, and a second motor in the missile
Launch motor can be seen trailing the missile in this image:
In general, two stage rockets are more complex, expensive and while they're more fuel efficient in the terminal stage, they're less efficient up front. In the end, it's a solution in search of a problem when single stage missiles get a sufficient PK as it is