Transposing keyframes or recursive keyframing in AE
Duplicate your composition twice. Let's call these 1, 2 and 3

In 2, replace the embedded clip layer with 3. With Alt held down and the embedded clip layer being selected, drag 3 on top of it. In 1, replace its embedded clip layer with 2.

I assume that the dimensions of the source clip and the composition are the same, else some transformation will be required.