Overview:
The main point of this challenge is to play the game with a rather... unusual family dynamic. And technically I wouldn't call this a 'challenge' so much as a different playing style since it's not that hard once you get the hang of it, and I openly encourage people to experiment with variants and different rulesets. What I'm posting here is better treated as base material.

For all you storytellers out there, and those who just like things to make better sense, it would perhaps help you if I noted that I came up with this idea after watching way too many documentaries about tribal peoples and the interesting ways that they live. But it also works to picture your Sim family as being some sort of alien race, hippy commune, or perhaps some extreme religion.

Set Up:
This can be played in almost any world, as that doesn't really matter. It does presuppose that you've got ready access to neighbors - it's easier to play in a built up world than an emptier one, but then again if you're used to emptier worlds then you're probably used to the problems you'll face.

Once you've picked your world, you need your initial household. You can either create it from scratch, or if you really wanted to you could bring together one made from Sims already in the world - either by using Edit Town, or if you really wanted to you could have one Sim befriend and invite the others to move in with them. But, however you get there, you to somehow end up with four Sims that fit the following criteria:

The first should be a teen or young adult near the beginning of that life stage.
The second should be a young adult or adult who is the opposite gender, unrelated, and preferably quite a bit older than the first.
The third should be a young adult or adult who is the opposite gender, unrelated, and preferably quite a bit older than the second. (But they could be a relative of the first if you want.)
The fourth should be an adult or elder who is preferably quite a bit older than the third. (The gender and relatedness of this Sim doesn't matter in the first group of parents, since they won't be having any kids with anyone. But if you want to follow the pattern, they should not be related to the third and be the opposite gender.)
(Note: When I say 'quite a bit', I mean 'at least 14 days' if you've kept your Sim's lifespans normal. If you've messed with the numbers, you figure it out!)

Things like life fruit and young again potions may help, but the easiest way to start is to simply make a household with one teen, one young adult, one adult, and one elder. But once you have your first four, you're ready to go! Have your four Sims respectively assume the duties of the four ranks as explained below.

Gameplay:
Your Sims are strong believers in the idea that children deserve to have everything from their parents. So much so that they don't believe that it's possible for even two parents to give their children everything they need. Therefore they live in a group of four so that they can pool their resources and provide better for the children. Every child born into the household is considered to be the child of all of them and is treated as such. (Whether or not they consider all the other parents to be their spouses or not is up to you...) To help keep things organized, each parent has their own role and set of duties in the household, but the others are quick to step in and help if one of them becomes overloaded.

Role #1 - The Initiate
This is the youngest of the four parents - so young that they may not even be of age to actually be a parent yet. But this is a stage of preparation. If they're still a teen, they go to school but come straight home afterward - there's almost always work there for them to do! Their duty is to maintain the household: they cook, wash the dishes, make the beds, do the laundry, feed the pets, clean everything, etc. If they have all of that in hand, they help with the children. And if even that is under control, they occupy themselves with some sort of self-improvement activity to prepare themselves for their future roles.

Role #2 - The Caregiver
This is the second youngest of the four parents. Their primary duty is the household's children - caring for the babies, caring for the toddlers and teaching them their toddler skills, helping the children and teens with their homework, etc. When they've managed to make all the children happy at once, they similarly care for the other parents or work on skills. If there aren't any babies or toddlers in the household, they use the school hours to help the Initiate maintain the house, work on skills, or may even get a job if they can find one that's strictly during school hours. However, the second that a new baby is born, it's back to being a caregiver 24/7. In fact, when the caregiver is a female, this is the best time for her to make babies, though if there's room for more and the caregiver is male, he can always seduce the Breadwinner or the Initiate...

Role #3 - The Breadwinner
This is the second oldest of the four parents. Their primary duty is bringing money into the household, whether that means working a regular job or through some sort of a lucrative hobby. When they're not working, they spend most of their time trying to improve their chances of getting that next promotion. Such single minded focus means that they don't spend much time with the children, but it takes money to keep the household running and supplied with all the things the children need.

Role #4 - The Head of the Household
This is the oldest of the four parents. Their primary duty is to make all the major decisions in the household and ensure the future of the family. Usually they retire at this point. When they first become Head of the Household, they're the one who finds and convinces a teen or a young adult who is known to be very young (who must be unrelated to and the opposite gender of the Caregiver) to join the household as the new Initiate. (You can do this by either inviting them to move in, or using Edit Town if you really want to - but if the latter, they should make friends first.) They also encourage the teen children to find a boyfriend or girlfriend - they want grandchildren! And they also keep touch with any Sim who was born within the household - even if it was before the current Head of Household's time, is still considered their child after all and they want to make sure that they're having a happy life! And in their spare time they do whatever they most believe will benefit the family - for some this means growing a garden so that the family can eat fresh produce, for others it may mean making sure that every child gets their own puppy. (I suggest using their traits to determine what they care about.)

Every time the current Head of the Household dies (hopefully of old age), the other three parents move on to the next role and they all help out with the household chores until a new Initiate is found. In the case of an untimely death of one of the others, the current Head of Household finds a suitable replacement. If one of the parents is some sort of supernatural entity that has an extremely long lifespan they still progress through the ranks with the other parents, but when they become Head of Household they eventually move out when the other parents are ready to assume their next roles so that the family can progress.

Of course the four parents pride themselves on their children, and expect nothing less of themselves than to launch each one of them into the world fully prepared to tackle it the moment they're old enough. This means that shortly after each of their children becomes a young adult, they're expected to be in some sort of steady relationship, have a starter position in a good job or profession, have a large set of skills that will help them succeed, and the parents also ensure that they have a decent place to move out to - helping them buy a new home if need be. Each young adult so supplied is moved out as quickly as possible to make room for more babies. Note: It's possible for a Sim who was raised in this household to become the next Initiate if they're a teen and otherwise qualify when one is needed, and in that case they don't need to move out.

Winning:
It's theoretically possible to literally play this forever (or until your save game glitches - whichever comes first). But if you want a set end point, 4 Heads of the Household is equal to one generation in most generational challenges. Thus, if you want to play the equivalent of 10 generations, that's 40 Heads of the Household, or if you want just 5 generations, that's 20. Which may sound like a big number, but switchovers end up happening on a regular basis.

This is an interesting gameplay suggestion, but as it's not really a challenge, I have moved it to sims discussion