You got me, this cutie is mine!:

I don't have one of my own that's grown just yet, and I don't have a name or dress-up to suit them yet either,
but I will provide that here once I do!
As for the analysis of my riddle, some of you did well, others were a bit off... that's the fun of it :)
My siblings think thrice, or sometimes foreverReferring to the fact that the chimera is related to Cerberus (three heads) and the Hydra (multiple heads/infinite heads)
But we prefer to depend on twoEven though the snake is technically a third head, I like to think it's just using the two
The Illiad, Prometheus, heroic endeavorsThe Illiad is where the chimera hails from, and Prometheus is referencing the fact that the chimera breathes
fire--threw you for a loop with that one ;)
Heroic endeavors ties back to the mythological roots
Scales of magenta, viridescent, and robin egg bluesRefers to the wings of the adult growth and the snake on the pup!
Thank you all for participating in guessing this friend!