Inside a metal electrical box, can I use multiple ground clips (one for each conductor), or is it required that all ground conductors be twisted together and pigtailed into the same clip?
If you are carrying ground from one cable to the next, you should pigtail them. The ground clips are there to ground the box, not carry the ground to another cable; if one were to become disconnected, you would lose the ground in the circuit.
I prefer a screw connection in metal boxes over a ground clip.
Oh, and instead of a pigtail, you can use one of the green wire nuts with a hole in the center; that lets you pigtail with a bit less effort.