Eh. I feel like dual-types are already stronger than single-types; the extra weaknesses are more often than not balanced by extra resistances, and dual-typed Pokémon generally have more powerful and versatile offensive skills because they have STAB on two elements. Provided you avoid any triple-weaknesses (which wouldn’t be that common; hell, against 1/3 of all attacking types it wouldn’t even be possible), I think triple-typed Pokémon would in general have an unfair advantage – unless you changed some of the games’ other underlying assumptions about type; you could do away with single-typed Pokémon altogether, for instance, adding a second type to all of them, or you could reduce STAB from +50% to (for example) +35% for dual-types and +20% for triple-types. That might make things interesting.
In terms of the idea of it, apart from the mechanics, well, I’d go for it if I thought the two-type limit was a constraint on the designers’ freedom, but I don’t, really. Giving a Pokémon abilities like Levitate or Swift Swim can already convey an affinity for or link with a particular type without having to actually add the type itself. I don’t think we lose anything by not having that option.
Having said that, you did ask, so… Gyarados as Water/Flying/Dragon would make sense, switching to Water/Dark/Dragon upon mega evolution; Flygon could become Dragon/Ground/Flying and swap out Levitate for something else (watch out for those x8 Ice attacks, though); Jirachi I think would make sense as Steel/Psychic/Fairy; Stunfisk really should be Ground/Electric/Water; Yanmega maybe could go to Bug/Flying/Dragon (‘cause, y’know, dragonfly); Dragalge could be Dragon/Poison/Water… there’s probably a few more I’m not thinking of.
Pokémaniacal 