Is there any Catholic lay movement centered on building Intentional Communities? An Intentional Communities is

a planned residential community designed from the start to have a high degree of social cohesion and teamwork. The members of an intentional community typically hold a common social, political, religious, or spiritual vision and often follow an alternative lifestyle. They typically share responsibilities and resources. (Wikipedia)

Catholic monasteries are examples of such communities, as well as Christian denominations like the Anabaptists (with the Amish being perhaps the most well-known example). A Jewish example are the kibbutzim.
My question is about lay Catholic intentional communities organised systematically (perhaps with some form of Rule). All I can find are individual self-organised communities (for instance, here and here). Anyone aware of more formal groups around this?
Taize would fit the criteria. It is a community that includes Catholic monks but also others, and is definitely run as an intentional community.
I believe L'Arche might also fit your criteria. While not explicitly Catholic, it was founded by a Catholic, and is certainly an intentional community.