Too confusing. It would be interesting though...
Many would fail in the category while slight improvements would occur in this same way, up and down. Bugs are pathetic they almost cry out "I am a little bug pokemon, step on Meeeeee!" 3 types would benefit them but not other pokemon so much.
FAIL
Gyarados - weaknesses now: electric 4x, rock
after applying dragon: electric, dragon, rock, ice
Good enough
Venemoth now: fire, rock, ground, flying, psychic
after applying flying type: fire, rock 4x, psychic, flying
Fail/okay
Masquerain now: fire, rock 4x, electric, flying
after water: rock 4x, electric 4x, flying