On the topic of multiple time players, maybe there is a chance that there are as many scratch constructs as time players. However, the key is to initiate them all at the same time (very unlikely though), allowing for several new Post-scratch games to exist at once. If it ends up like anything with the Beta/Alpha kids, then the sessions are merged together for one huge session. Something like [s] Collide, but on a huge scale.
Ooooh, or how about, rather than multiple different Scratch Constructs, the Scratch Construct is divided in 4. You need to Synch up all the parts to use it properly. What kind of device would this even be? With Music Boxes and Records we know there’s a trend towards music-storing devices, hmmm…