I saw the movie R.I.P.D. last night - it's very silly and got a lot of negative reviews, but I personally thought it was quite good fun. What I really noticed was that there are a hell of a lot of similarities to the basic ideas of the TV series Dead Like Me.
In DLM some people who die are selected to become Reapers, who collect people's souls just before they die to ensure a smooth passage to the afterlife (which seems to be whatever the dead person wants it to be). It's mentioned that if a soul isn't reaped it stays in the body and quickly becomes a monster, a psychopath or worse. In R.I.P.D. the main characters are cops who have died but are assigned to round up "deados," dead people whose souls have somehow avoided collection (in this case by being drawn into the sky by some sort of vortex); again, escapees become monsters, although this is physical as well as mental. In both the living perceive the dead as different people, so that they can't be recognised by anyone they knew before they died. In both it's apparent that the system is overloaded by sheer numbers, with huge population growth there are simply too many people dying every day.
So the idea I have here is that the Reapers handle the normal cases, with the RIPD going after anyone who falls into the cracks. They don't normally come into contact because there simply aren't that many escapees. Except that in RIPD there's an organised conspiracy for the "deados" to stay on Earth disguised as people and take over the living world - exactly why they think this is a good idea isn't made clear. But as it gets under way the Reapers will start to see more and more failed reaps; this is going to put them under a lot of pressure, and maybe lead to mistakes.
What I'd like to see in a crossover would be the essentially peaceful Reapers forced to work with the RIPD, who are essentially trigger-happy lunatics with badges. Maybe Reapers are assigned to the RIPD to show them what happens when they mess up, or an RIPD cop gets sent to work with the Reapers as a form of sensitivity training. Maybe Roxy (the Reaper whose day job is a cop) is actually an undercover RIPD operative, sent to find out why the system isn't working as well as it should, it wouldn't be that big a personality change. Think "very miss-matched partners" buddy-cop movie and you probably won't go far wrong.