No, actually it doesn't happen if you enchant multiple creatures. If you have 3 Stag Hearts on 1 creature, that creature will be +9/+9, but if you spread those 3 Stag Hearts across 3 creatures, each creature will have +3/+3. I have no idea what would happen if you put 2 Stag Hearts on Creature A and 1 Stag Heart on Creature B. But here's the text of Mojang's response to my ticket.
If they added +9/+9 to each of 3 creatures, it would sum up to a total of +27/+27. It is still broken, and very overpowered, especially since you can put that on a Relentless creature and just destroy everything, and unless your opponent has a way to reduce the movement to zero, or Pushback, there's no way you can stop that creature from slaughtering your entire army.