The gag is a simple one and derives from some common conventions: a young prince and warrior of the realm might be eligible for governance when his lordly father passes away but his aunt the duchess or his uncle the vizier or whatever frames him for poisoning his father and banishes him, along with any soldiers/guards/servants/retainers loyal to him. This ends up being a far larger number than the Bad Guy expects so they are forever fearful that this aggrieved retinue will one day return, even while under threat of death, perhaps after raising a larger/stronger army. To secure their power base the BG sends out mercenaries and assassins and brainwashed warriors and unwitting NPC adventuring parties all out after the prince and his followers.
This necessitates a peculiar survival strategy.
The prince and all his assembled loyalists split up into groups of four, each of them identically outfitted and groomed, each of them identically armed, and spread out through the land. Even if you find one of these cells, you will have no idea which one is the real prince and which ones are the loyal imposters. That's assuming the real prince ever even is in the group that you find! These days he calls himself Oom and, therefore, so do the servants following him. Occasionally an enemy is successful in striking down the man purporting to be Oom, prompting another retainer to step forward and declare they were the real Oom all the time, taking up his place.
Next time they're in town this trio will be seen drinking in a few bars and the next morning they will be four again. A life of adventure or simply a life outside of village drudgery that comes with the added security of three men pledged to watch your back and the promise of favors should the kingdom of Oom ever be rightly restored? A tempting offer for many a townie, and indeed many a veteran and guardsman. There are warriors everywhere if you know where to look and when there aren't where do warriors come from in the first place except for where Circumstances meet Will?
This is in fact a popular enough strategy that other bands wholly unconnected from the original loyalists have adopted it, traveling the countryside as Ooms. That's not to say that all Oom bands are identical - some may be dressed for Sherwood Forest, others dressed for Kyoto - but while height and weight and countenance may change they are within the band. Even bands of orcish Ooms or Oom women are not generally remarked upon because this story has been kept so deliberately vague, the details so changed from band to band, that who's to say what the real original story was? Maybe there never was an Oom.
Of course there was, and they're still out there doing their thing, but the Duchess Or Whatever never needed to worry: they hated that kingdom and are glad of the back of it, having a blast playing a cup and ball game with the entire world, and never had any intentions of going back.
Oom bands will sometimes run into one another, mix, and separate, to keep things fresh. Other times one band may send for help or counsel from one or more other quartets. These are kept rare when not in outright crisis: staying apart is a key piece of the scheme, after all.
In 5e you can do this really easily with only class and background features, never mind feats to round things out. When it comes to LotFP you just kind of buy them along with your gear. For both of these in the interest of fairness I think you have to pay for every piece of equipment and food for all four in your band and keep that up as you progress, which gets easier. And you may have to go a while with an incomplete group. I'd also say in the interest of fairness only one person in a group should be actively fighting and doing PC shit, though the rest can help like watch for people following your carts or help break camp or climb over a wall.
In Feng Shui (2) I just used the Ex-Special Forces type and just changed the skills and weapons to make them more period appropriate. In FAE I just make these whole core concepts into Aspects and take the "You didn't get the original Multi-Man!" shit and turn them into Stunts 1/session. I have never ever had a human say "Let's play Fate" in person (not "have you tried FATE" but "FATE seems like fun let's play it") but enough of my friends purportedly appreciate the idea of playing it that I have it on hand.
Keep in mind that losing an Oom and having the 'real' Oom step forward means starting from scratch with XP and advancement and shit, they just retain knowledge of what has gone on so far. So it's the same character but it isn't, and they likely have different ability scores and shit where the DM feels that's fair. Honestly the version in my wallet has good-but-not-great scores so I think he's fine.
This is just a reskin really of the old gag where your dwarf Gunnar dies so you cross out his name at the top and a dwarf named Sigmar with the same starting gear walks in from the next room and now he's in the party and he picks up all of Gunnar's stuff, but it's got just enough to it to turn it into a weird setting detail, encounter table entry, quest hook, or tavern rumor. It's also a reliable way to pick up backup for a big fight or a dangerous delve.