I a huge fan of the film. I have no idea how this would be turned into a series. Take away Gilliam's style and the fixed time loop, sense of doom imediate doom what else is there?
Only thing I can think of Willis' character was mistakenly sent to the wrong time periods. once to a decade earlier and the other all the way to the First World War. Plus there was another travel sent to comin ate with him. Guess they could expand those ideas. I doubt this will last long.
There have been a lot of efforts recently to have time travel series. But they never move beyond a poilot or a short run. Usually because the premise is limited to create interesting stories. they need to bring Back Quantum Leap or something similar. That has endless possibilities for period times and stories.