For more institutionalized settings, there's co-op daycares, but we looked into this and they're largely incompatible with having two working parents since the schedule usually requires volunteering in the middle of the workday.
What little there is can usually be extended to 1 or maybe 2 kids. We routinely have 4 kids at our house (2 ours), but nobody will be able or want to manage more than that, and not very frequently. Even that sort of arrangement only happens via trusting friendships that are built over time. Distributing the load across multiple arrangements would be logistically daunting.
Perhaps a religious or cultural group would extend their resources in this way, but you would have to belong to those groups, and even there, nothing is free.
And one more thing: any place in the Bay area where you can find a house large enough to comfortably house 6 kids in a relatively safe area is going to be unbelievably expensive. I'd you live in such an area your neighbors will either have many fewer children or be wealthy enough that they hire full time childcare, so they won't have the same needs for village style arrangements as you.
So the problem is a bit of a prisoners dilemma: you need to be able to rely on this group (having to scramble to find another solution is OK a few times a year, but not 3 times a month), but you also don't want to be 'tied down'.
So the alternative is to have lots of rules and required 'volunteering'. Which basically turns into the same as 'real' daycare, except that you have to take the day off to do your 'volunteering' (in the case of 2 working parents). So it's just scrambling to solve all the problems that money is supposed to solve (be a fungible store of value), but while at all costs keeping 'money' out of it.
Having been involved with attempts at systems like this, and having observed the problems in a few others, I no longer think it's feasible, at least not for dual income career oriented people. The places where I've seen it (more or less - it wouldn't work as a lifestyle for me) work are of the type of the mommy group of stay-at-home-parents, but those are hardly comparable to real daycare.