This isn't a full fledged idea just something I thought would be interesting.

In an early level the player needs to move about the level collecting items. Then there is a later level where the player has traveled back in time to place the items that were collected earlier. But they must avoid their earlier self, if seen you've created a paradox and lose. Additionally if you don't place an item in the right place before your earlier self collected it, you also lose. Basically your earlier movement through the level is replayed for you to avoid.

Potentially allow for the player to replay the earlier level should it prove to difficult to avoid the earlier self.

Edit

One thought is anytime the player opts to redo the first level the collectibles are randomly placed throughout the level. But they stay in those locations for the later time travel level. Just a reshuffling (but this might be overkill)