Every >1 death rate scenario I can think of either reduces to the very long life-spans version (everyone is Jack Harkness; Time Lords) or partial-reproduction-by-fission (Homestuck AU).

Or you do something like, after first death you become a ghost or a ghost-in-the-machine, but when the stage between first and second death has so many different physical properties from the earlier stage, i feel like you could go pretty much anywhere in terms of social structure in that scenario.