As others have said, as long as you keep casting it on the same hero, the effect will stack but the mana cost will keep increasing. If you keep stacking it eventually you just won't have enough mana anymore. If the duration runs out just once all the stacks are gone instantly and you have to restart stacking from scratch.
If you're playing Murloc yourself, it's a good idea to start stacking attributes on yourself once you get Anfibius Growth Level 3 or Level 4. Level 3 is more difficult to maintain but getting last hits on creeps is so much easier if you have a few stacks, and if you do manage to maintain it you can start doing neutral creeps that much sooner.
If you're at a higher level it also becomes manageable to stack attributes on someone else and not yourself.