With one group in the pattern, you can only get one exact result in that group. If your capture group gets repeated by the pattern (you used the + quantifier on the surrounding non-capturing group), only the last value that matches it gets stored.
You have to use your language's regex implementation functions to find all matches of a pattern, then you would have to remove the anchors and the quantifier of the non-capturing group (and you could omit the non-capturing group itself as well).
Alternatively, expand your regex and let the pattern contain one capturing group per group you want to get in the result:
^([A-Z]+),([A-Z]+),([A-Z]+)$
^([A-Z]+),([A-Z]+),([A-Z]+)$
