To Unlock More summons you must earn Artifacts and sell them to the Bio-Lab.
Summons Use SP to Act. They use 4SP to Attack Physically, and 6SP to attack Magically.
Summons have 5 Levels, but do not gain EXP, instead they Level through AP:
Level 1: Creature (Default)
Spoils for Each Level will Vairy for every Summon, they will get HP/PA/MA boosts, and an Ability upgrade.
For a Summon to Gain AP, they must be used in a Quest, or Iron Gauntlet, or even Storylines; However, Summons cannot be used in: Duels, Gauntlets, & Cage Gauntlets. Summons gain the same the AP as their Owner, but only if they are Used at least once.
Summons may also gain Special Attacks that require 10 or more SP to preform, to gain these attacks, you'll have to use Artifacts, or Relics on your Summon in a Lab. This can be done in a Global Bioporta Lab (Locations: Narcio, N. of Skinka, Tarjin, & Linghai), or in a Personal Lab, either way you'll need to get the Bio-Tech License (200g).
Some Summons can be Unlocked with Stolen Items, that may seem useless, so be sure to try and steal from every enemy once. (You can Steal in Quests, and Iron Gauntlets; Stealing Requires that you first learn the Theft Lv1 skill).
When a Summon reaches a new level it will gain pts (points), you the owner will get to allowcate where the points go in your summon's stats. Each Type has a set number of points that it will earn.