So far as I've found, no. If I've missed something on the typing list, please tell me, but I can't see any possible combination of existing typings and abilities that will cancel out all weaknesses.
Considering that grass is weak to Flying, Ice, Fire, Bug and Poison, there's no Pokemon combination that resists all of them.
The closest I've found:
Empoleon - Ground, Electric, Fighting (only Fighting weakness remains)
Tentacruel/ Qwilfish - Ground, Electric, Psychic (only Flying & Psychic remain)
Rotom-W/ Lanturn - Ground, Grass (only Bug & Poison remain)
Grass typing just has too many weaknesses for any typing to cancel out all 5 of its weaknesses as well as the original weaknesses.
Steel/ Fairy + Grass with Flash Fire
Original weaknesses: Ground
Fire is x0 with the ability
Poison x0 with Steel typing
Flying & Ice both x1
Is the only one I can come up with. Steel/ Ghost with Flash Fire would have worked before Gen VI, but now that Steel no longer resists Ghost & Dark, it doesn't work.