I had some time on my hands and made this list of potential type-electives of the senior and junior students, don't know if we get more types with the years so I kept it at max. 4. Also I did not really go by the personality-type connection so... yea.
Brock - Rock, Ground, Water,
Roxanne - Rock, Normal, Steel, Ground
Brawly - Fighting, Water, Steel, Ground
Janine - Poison, Bug, Dark, Fighting
Clemont - Electric,
Erika - Grass, Poison, Fairy,
Falkner - Flying, Ghost, Grass,
Korrina - Fighting,
Yellow - Electric, Bug, Dragon,
Ethan - Fire, Normal, Rock, Dragon
Silver - Poison, Dark, Ice, Water
Wally - Psychic, Fighting, Normal, Fairy
Lucas - Grass, Normal, Ground
Barry - Fire, Normal, Fighting,
Dawn - Water, Psychic,
Candice - Ice, Grass, Normal, Ghost
Maylene - Fighting, Psychic
Tate - Psychic, Rock, Fire,
Liza - Psychic, Rock, Ice,
Nate - Fire, Fighting,
Rosa - Grass, Normal,
Hugh - Water, Dark, Normal
Iris - Dragon, Ground,
Kris - Water, Normal, Psychic, Ghost
Lyra - Normal, Fairy, Water