So far, the campaign is lethal and we have had a series of people joining and quitting.
A party member came up with the idea of creating an organization who can continue on the adventure regardless of who joins or leaves.
How would you structure it?
I actually created a homebrewed Treasure Hunters Guild, and it works like what you are asking for.
1) There's the guild, which means there are tons of people. If a guildmember (PC) decides to take up a quest and not finish, it makes sense that another guildmember (different PC) can resume where they left off. If 1 member leaves, the party can send word for a request for more assistance. PC's can switch off between different members of the guild, assuming who they want to switch to is still alive. That solves the problem with having many different players, or several characters per player. I only allowed 1 character per player, per quest. When a quest finished they can switch to someone else for the next one, unless their character dies then they can switch immediately.
2) At the beginning of an adventure the guildmaster, or someone of higher influence, will present several quests for the party to choose from. This works great if you want to run modules/scenarios. The guildmaster will give a quick overview of each quest, only revealing info he knows of, along with how difficult it might be. The party picks what quest they want to do, and then they are on their way. Or perhaps a quest will start more eventfully in the middle of the city, and the party can follow through if they wish. The hard part about this is you need several quests prepared at once.
3) I specifically chose the "Treasure Hunters Guild"(True Neutral) because treasure can mean different things to different people. The treasure you search for may be of riches, love, power, honor, fame, or something else. This idea gives good motivation for the guild to offer many types of adventures, and for people with different goals to join. However, the guild you want to make is your choice.
edit:
#2 and #3 are totally optional of course, but #1 will work great to solve the problem you are facing. I would just be careful that players don't abuse the system. There should be realistic restraints, like less rewards if a quest is abandoned. Or if a new character is requested the new player has to wait a certain amount of in-game days for every X amount of miles the party is away from the guild. The time a player is waiting is the time their character in-game is traveling to the parties current location.
Any organization or combination of groups can achieve what you're looking for. Some examples:
The Ratcatcher's Guild: once a simple city guild for sewer/sanitation pest control, it has blossomed into legion of mercenaries, bounty hunters and sell-spells who ply their trade specifically to seek out and destroy "rats" be they monster or mundane.
The Order of the Weeping Maiden: the threats to the Beloved of Pharasma are many; undead, the hordes of chaos, rogue wizards and brigands. One paladin long ago made a stand against these foes and she died weeping over what she left undone. Over the years many statues of the paladin have been crafted and dispersed; when they weep, the Beloved gather. Now it is known that the Weeping Maidens foretell some evil and the Beloved of the Order watch for the signs - when the omens are right and the weeping begins, they dispense agents to deal with the threat.
The League of Grimm: born of the pursuits of a pair of legendary hunters of fey and the supernatural, these scholars and adventurers mean to end scourges to the land proposed by these creatures. They have hidden repositories of lore scattered throughout the wilds and rural communities and their agents hide in plain sight. You don't join them... they join you.
The Inkswill Pub: Farluss Bandovier Inkswill was a lover of 3 thing - Magic, People and Beer. The Halfling wizard used his power and influence to craft a Public House or "pub" where likeminded individuals could gather with him from all over. Unfortunately for Inkswill, he was not well loved by the local government. And so the pub was moved WELL outside the city... to a nether-realm of his own design. Since then doors to the Inkswill Pub have randomly appeared in the most bizarre places; dungeon delves, deep under the sea, and once on a cloud giant's pleasure skiff. The point though is that all are welcome, so long as they make no trouble in the pub and serve the greater cause of the place: resolving conflicts among people.
The Ironmourn Company: this mercenary guild is known for 2 things; fighting and drinking. Unfortunately, this is nothing more than a ruse. The real purpose of the Company is to recruit and dispatch agents through the land to pursue a secret inquisition against the witches and their minions. The mercenaries have a public face in their Ironmourn Citadel but teams under their banners are likely to be found carousing and traveling far afield. For a fee ANY can hire their services, but just as often darker patrons find that after employing the Ironmourn Company their fortunes turn from bad to worse.