Running Parallel Campaigns
My experience with running parallel campaigns mostly involves the World of Darkness games, Aberrant, and Call of Cthulhu. Some ran longer than others. The WoD games lasted years of real time, and were designed to be open-ended.
I used Vampire: The Masquerade as the baseline game, with players in three separate factions (Camarilla, Anarchs, Sabbat). Added to this game were additional weekly sessions with different players in a Werewolf Chronicle in the same setting, monthly sessions with different players in a Mortals Chronicle, a weekly Mage Chronicle in the same setting, an infrequent Mummy Chronicle, and a small Wraith Chronicle. In Aberrant and Call of Cthulhu, I ran sessions designed to be of a more structured and much shorter duration using the same settings but with players in various locations both in reality and in the game world. This was a method of maximizing preparation time from my D&D days where I had several small, regular groups of players that could not meet at any set time or place to play together.
Problems common to each campaign
The biggest issue overall I had to face was one of keeping the rate of progress between each group consistent. Many elements can be recycled for each group, such as news reports, rumours, signs, portents, and so on so background preparation is less intensive than you might expect. Your main story threads do need to be very distinct to allow your players the freedom to operate without conflict from the storylines of the other group(s).. Geographic separation is often essential for this to work, but vastly different social status or networks can accomplish the same goal.
Cautions for characters in a shared universe
When storylines overlap there are pressures to use PC characters from other groups as a temporary NPC. This can upset some players, so it's something to be discussed beforehand. From the outset, it is best to decide once and for all if the game universes are the same or separate. You have the most freedom and safety if you choose to have them exist separately, but miss out on the very exciting opportunities for cross-over. There are pros and cons to using and not using PCs as NPCs in other groups, having guest appearances by members of the other group during nights of heavy involvement with that NPC, and developing alliances or rivalries. These decisions are not ones that you should make on the fly. Consider them carefully, and consider the personalities, and personality interactions among your players.
Cross-overs: A useful, short-term benefit
Some examples of manageable and useful cross-over between groups from TV are X-Files and Millennium, the various characters from CSI visiting one or more of the other cities, characters from one Star Trek or another mingling with another crew for reasons of age, change of service, transfer of assignment, time travel, etc, and federal law-enforcement working with characters in a state or municipal jurisdiction with locally based characters.
A great moment from my joint Vampire, Werewolf, Mortal, Mage , Mummy, Wraith Chronicle was when characters from three of the five distinct storylines all came together to either support or oppose the return of a rival Vampire Prince. Players went into the session knowing that there might be PC vs PC interaction and that the session would change many things about all the settings for good or ill (from their perspective). It was like a combination of sweeps week and a season finale. Those not comfortable with going up against other players given equally important tasks to do, but away from the 'danger zone.'
Competition: A benefit or a curse
Either in a cross-over or in indirect competition by working on the same puzzles and storylines in games with the same setting, but in a different game universe competition can be a wonderful motivator, or a massive problem. Not everyone likes to compete, and many who choose to roleplay do so because they enjoy games, but do not enjoy being in direct competition with each other. Introducing members of another troupe of gamers operating in the same universe can backfire for out-of-game reasons, or it might light the spark which really gets both of your groups invested in the tale. Communication and observation are the
keys to discovering which you are likely to get.
Final Tips
This style of campaign will require you to set up the world as a sandbox, and be very aware of relationships, the passage of time, and the rate at which information can reasonably spread. The more you develop the world as an open sandbox with its own events, actions and reactions, the easier it will be to manage in the long run.
It is definitely worth trying if you have the interest and the players.
Be an NPC, not the GM
The GM, as an entity, must be infallible to a certain degree, because he is the PC's conduit to the game world. If he says the party meets an NPC, the party is now reacting to this NPC. If he says here there be dragons, the party stocks up on burn ointment. Players are likely to feel betrayed if this turns out to be false - not false in a "the princess we were sent to save is the dragon we need to save her from" but false in a "my combat guy has no skills relevant to a campaign centered around gangster rap battles" way, or an "I took an evening of my time to come roleplay a courtly flower arranger, not punch out Cthulhu as a superhero" way.
Enter the unreliable narrator. The GM needs to be infallible, but the NPCs need not be, so you can avoid the backlash by blaming it all on a made-up guy. If you are exposition-dumping, feel free to use crazy old man McGuckett as your mouthpiece. If he says he saw cultists summoning demons in the swamp, that's what he thought happened, but it's not the GM's fault the PCs took his word for it. Or he was lying and the PCs are now about to be ground into mincemeat at McGuckett's terrifying shed of rusty chainsaws and leather masks.
This works great when you can have an NPC travel with the party, and be their eyes and ears in terms of a certain task. A party of samurai may be escorted by a local shaman who claims to talk to the spirits, but in actuality is just making things up as he goes along. In an urban adventure, a lawyer, accountant, or other suit-type can string the PCs along in a nefarious scheme, or a scientist can ask them to do progressively stranger things...
Player vs character knowledge
Another issue is that your player's first session behind the sheet of Winnie the Wizard isn't Winnie's first day alive. She's lived in her world for decades, and it's not wrong for her player to expect that the GM will tell her things that Winnie knows but the player does not.
This one is actually very simple to fix - engineer a travel episode that sees the PCs arriving in an unfamiliar land. This will also help by gradually introducing the genre shift and making the PCs feel like it wasn't sprung on them.
One reflex might be to bar all kind of character knowledge, but you can actually use it to your advantage if you do it right. The perspective of a stranger in a strange land helps reinforce things that the players might not find weird, but their PCs sure as hell should. For example, your players might not know what color magic is supposed to be, but as soon as Winnie casts her purple spell and it comes out green she knows that something is afoot.
Best Answer
That article doesn't come out and say it, but the ultimate goal of petitioners is to become their deity. Sort of, anyway. See, a petitioner who dies faithfully following their deities' precepts loses their memories, like you've read; What you haven't read is that the memory-less soul that's left has the sole goal of pursuing that deities' philosophy. Eventually, the petitioner comes to understand, embrace and embody that philosophy so completely that they think about and react to things exactly the same way their deity would - and that's the point at which they merge into them.
This means that petitioners of the same Power all have a simple and easy-to-understand goal, and only differ in what they're "missing" to reach it. You could say there's just one question you have to yourself about each player character to determine whether they'll have a motivation to pick up your plot hooks: "Will doing this bring her closer to who she's trying to become?"
You're therefore going to want to pick a Power for the PCs who is broad enough to support a wide variety of classes while still allowing all the PCs to gradually progress towards the same kind of personal ideal. That ideal also has to be compatible with adventuring, so something like a deity of protection or community might be a good bet.
When petitioners go in the dead-book, they're deader-than-dead. As in, the bashers are gone. Forever. No way to bring 'em back. If they're still on the plane they went to when they died, they merge with their deity or plane a little ahead of schedule; If they're on any other plane, the poor sods cease to exist. Oblivion embraces 'em, and whatnot. In other words, no matter what plane a petitioner is on when it shuffles off the post-mortal coil, raise dead and resurrection are off the table.
You might want to modify that for your campaign, or you might not. It's something to think about.
Other than that, the only special rules changes relevant to running an afterlife game are the standard Planescape ones, and rather too extensive to replicate here. They mostly affect magic items and spell casters.