If a couple is a pair or a group of two, what does one call a group of three, four, etc.?
You're looking for:
.. and so on.
Beyond eight the numbers get a bit silly. If you're talking about music groups, you can use the counters "piece" or "person": a twenty-one piece orchestra, a twelve-person chorus, etc.
Note that "two" can also be duo.
Also see this question: Can I form a word like "quadruple" for any number I want?