There are actually 32 unique /r/ allohones, 42 acutally if you count medial /r/ blends as in words such as apricot. Here is the breakdown of the 32 unique /r/ allophones or sounds:
19 vocalic /r/’s where the vowel is before the /r/ as in words such as Archie, barn and father
11 initial /r/ blends a consonant occurs before the /r/ sound as in words such as bread, print
prevocalic /r/ words have /r/ at the beginning of the word as in red, run and race
medial/final /r/ as in words such as girl, world, swirl
Not all student misproduce all 32 /r/ allophones and the misproductions are usually separate. For example, students who misproduce prevocalic /r/ or words with /r/ at the beginning of the word also misproduce the /r/ in initial /r/ blends as in the word bread. The vocalic /r/ words in my clinical experience are not intertwined with prevocalic and initial /r/ blends.