Raising pet level of summoner auxiliary?

Is it possible? Is so, how?

Auxiliary equipment is a bit different than normal when it comes to how things are calculated. For Pets, all that is taken into account is the Rarity and Type of the Egg you give the Aux, and Level and Bonus Stats are not taken into consideration. Basically, if you want your Aux's Pet to be stronger, you need to give it one that is higher Rarity.