I assume you are talking about an arrangement where the children from several families spend quite a lot of time learning together - not just a few hours a week? They exist, but they aren't very popular here. People who aren't yet home educating often like the idea because it feels school-like and familiar, but there are challenges.
Compared with Americans, a smaller proportion of British home educators follow a very formal approach for many hours a week. And if you're going to be somewhat free and easy and let your child follow their interests and take advantage of whatever clubs and sports and home ed groups are available to them, you won't want to be tied to a schedule which dominates much of the week and may involve the kids learning things which don't interest them or using resources which don't suit them. Nor would you want to have to do all the work involved in prepping a "lesson" like teachers do if the approach you use with your own kids is more flexible and involves learning together as you go along.
There's also the very tricky challenge of finding children AND parents whose values and parenting/educational approach align well enough that the kids would want to spend that much time together and the parents would be content with way the other parents manage things. Not a big deal if it's a French lesson for two hours a week, but more of a problem if another parent is doing lessons with your kid for a whole day a week. That's intense. The co-ops I know of in my area are rather hush-hush because they don't want to be in the awkward position of turning people away due to incompatibility. When they have a vacancy, the parents will eye up the approach of other people at home ed groups, getting to know them quite well before broaching the subject.
You'd have to keep the number of hours low enough to ensure your arrangement isn't classed as a school, which makes it subject to onerous conditions.
What aspects of a co-op appeal to you? There may be other ways to achieve what you want.