Here are some more specific terms depending on the number of stars:

* Triple star system: 3 stars

* Quadruple star system: 4 stars

* Quintuple star system: 5 stars

* Sextuple star system: 6 stars

* Septuple star system: 7 stars

And so on...

For systems with a very large number of stars, astronomers might just use the general term multiple star system or multi-star system.