This has been asked before - in 2013 - in relation to smoke:
How to offset multiple smoke instances by time?
The answer was inconclusive, so I'm wondering if there's something new since?
I'd like to write a single particle cache to disk and read it back multiple times in different settings. It works fine using the 'External' option on a new particle system and I can even move the entire sim about in space with the 'Parent' feature.
So far so good. But can I move it about in time as well? Have it begin say 120 frames later? Perhaps someone has written a script for this?