Animation Viewer - Adding new elements to an existing Clip?

I'm currently trying to build and animate a 2D character made of multiple sprites, but I'm having trouble with the Animation Viewer; I'd like to be able to add new parts to the existing animation Clip whenever I need to.

I've managed to get three sprites on the same Clip by parenting them before the Clip is created, but I'm having trouble adding additional sprites afterwards. Parenting after work has begun on a Clip doesn't seem to work - keyframes will appear in the timeline, but the object itself doesn't appear on the dope sheet and doesn't move when the animation is played.

Please help!