I think that one character at a time would be sufficient, but if we are worried about deaths then we could pre-plan to have three characters in the wings to take over. Just like a DnD campaign, your character dies? Oops, oh look here is your cousin Bob here to take over. But also, this leads to another meta-gaming situation. If someone's character is killed, it would presumably be done by the culprit or associated with them. We could all read said murder, and we could then act off of that, whether our characters saw it or not.
I personally would stick with one character and one character only, makes it a much more risky situation. You have to survive and detect smartly, you know you are on the trail of a murderer you can't make any stupid mistakes and jump to any wild conclusions without proof. If they all die before figuring out who the killer is, well then, the murderer gets away with it. A realistic scenario, makes a way for the murderer to get away with it and 'win' too.
Beyond this, are all the players private detectives that have been brought in by the local governance to help out the constabulary, sleuthing for our own personal vendettas, or are we all working for the constabulary? Or shall we make this just a part of our individual characters backgrounds?
Hmm...I think I see what you mean...
The only thing is that I wasn't originally going to limit possible killing to just the culprit, but depending on the set of characters we end up with, I'm not certain whether it's a good idea or not. I guess if I put a limiter on the characters, some sort of device that generally keeps everyone wanting to keep as many members alive as possible, then maybe, but...
I'm still working it out. The whole 'character death' thing is looking to be the most complicated problem so far. I want there to be high stakes, but I don't want it to just be over too soon for any players if their characters just disappear before the end of the round. I at least want to give them something to do so nobody feels ripped off...
But yeah, an equal opportunity for the culprit to 'win' is probably a best case scenario. More reason to be smart about whatever the characters do. Gotta think about this more.
For the characters, I guess some of them could be part of some kind of official investigative group, but I think it would be more interesting if most of them didn't really have such a background. More of a 'detective by chance' than 'detective by choice' group. If anyone wants to add some experience to their background, though, I don't mind. Just not an entire party of them.
Personal agendas are good. I was just going to tie them all together with a common goal outside of 'find the dude, clear your name.'
