Co-op games where there isn't fixed trinity roles, but you can still build to play as a healer?

Guild wars 2 doesn't have the Trinity, each class is a bit of a blend, definitely worth checking out.

Gigantic: Rampage Edition

There's a lot of customization within each hero. There's no clearly defined role for each one, you can mix-and-match different styles of gameplay.

Albion and EVE have the ability to hop in and out of support roles. Albion is probably a better example.

GW2.