Here are all the types that have the same relationship as Grass, Fire, and Water. Divided into "true" starter trios, and "false" starter trios.

>True starter trio: Type A is SE against type B, type B is SE against type C, type C is SE against type A, type A is NVE against type C, type C is NVE against type B, type B is NVE against type A.
Fire/Steel/Rock
Grass/Ground/Poison
Fighting/Rock/Flying

>False starter trio: Type A is SE against type B, type B is SE against type C, type C is SE against type A. However, type A is not necessarily NVE against type C, and so on.
Fire/Grass/Ground
Fire/Grass/Rock
Fire/Ice/Ground
Water/Ground/Electric
Grass/Rock/Ice
Grass/Rock/Flying
Grass/Rock/Bug
Ice/Ground/Rock
Ice/Ground/Steel
Ice/Flying/Fighting
Fighting/Dark/Psychic
Fighting/Steel/Fairy
Ghost/Ghost/Ghost
Dragon/Dragon/Dragon