I'm going to guess that you enjoyed our April Fool's
, and want to discuss the general concept of adding additional stats to pets -- correct?
New stats added via stone upgrade would need A LOT of thought and testing. How many new stats would be implemented? How will they impact PVE/PVP? What effects/animations would they give, if any at all?
If it's not purely cosmetic, there could be some balancing issues. One stat would likely become most preferred for battle, just like a pet, strat or team becomes the 'go-to' for most. Blizzard would need to tread very carefully to avoid making an "OP" new stat.
In the end, I kind of see problems with this, similar to issues that we ran into with epic pet battlestone upgrades.
If you don't add X new fourth stat, you just won't be competitive or keep up in battles. That means upgrading your entire collection with a specific stat...and others have already mentioned (in epic battlestone discussion threads) how that method of upgrading doesn't sound appealing.