Since R214 most of the Pets in the game come in different "rarity" tiers. They can be upgraded using 
Altered Crescerite. Every upgrade increases the bonus you receive from the pet itself (bonuses for Collector's Bag completion are not taken into account). The following table lists the costs of upgrades.
| Upgrade from | Upgrade to | Cost |
|---|---|---|
| Improved | Magic | 5 |
| Magic | Extraordinary | 25 |
| Extraordinary | Legendary | 50 |
Common pets (pets without any state buffs) and Unique pets (pets with very special bonuses that are not meant to be further improved) cannot be upgraded.