How do I turn dynamics on and off through a single animation?

I want to animate an object, imagine a cube in the middle of the air at the beginning of the sequence; dynamics on, it falls to the ground and bounces a bit. Then I want to animate it manually to float up into the air again and then fall to the floor with dynamics again.

How do I do this? it seems like animating the “enable” tickbox or the dynamics on or off doesn’t help.

Another way I could ask this is, how would I manually animate an object after dynamics have already enacted (IE after falling to the floor.)?

Sample scene:
https://www.dropbox.com/s/vssn0jawsmbu126/cube-animate.c4d?dl=0

Thanks!