Desirous Maya is found in Block 5 of Tartarus, Harabah, from floors 191 to 200. It will be in the party's best interest to get rid of them before they start sapping the party's SP.
Desirous Mayas are later found in the second and third section of Antenora within the Abyss of Time. They will support the Phantom Master and Prime Magus by using their Break skills to strip away the defenses of party members that Null, Repel or Drain Fire and Ice attacks. Should they be the last shadow left on the field when their turn arrives, they will escape the battle.
Desirous Maya appears throughout the second Theater, Junessic Land. Its Maya Goop is used to unlock the Emerald Stick weapon for the P3P heroine, and its Maya Crystal unlocks the Coin Knuckles weapon for Makoto Niijima.