All I remember about this anime is a girl and her brother go to a boarding school (I believe) and the girl ends up uncovering a secret. The government is secretly trying to either destroy or control monsters.
She can control this bird-type monster that looks like a phoenix. A guy, probably an adult, who they met on the boat to their new school controls a dog-/wolf-type monster that might have been mechanical.
I watched this probably about 2009ish.