Rare Candy only allows Basic to Stage 2, so you'd still have to wait another turn.
Stage 3 Pokémon would not happen. Non-ex caps at 120 HP. Stage 2 Pokémon with 120 HP would gain nothing by evolving again unless all Stage 3 Pokémon were Pokémon-ex. You won't be finding some Stage 3 abomination with 160-180 HP with no drawbacks at all.
In the game, Stage 3 Pokémon are also not very feasible for most existing evolutions. They would evolve at extremely high levels, especially for Pokémon like Dragonite and Tyranitar. Their stats would be greatly increased to fit the new evolution, giving them near-uber status.