With the new Dignity additions — St. Mary’s Medical Center and St. Francis Memorial Hospital in San Francisco, and Sequoia Hospital in Redwood City — the Canopy network will have 4,000 physicians, 16 hospitals and about 15,000 patients, or “members.”

This means that any Dignity patient who gets insurance through Health Net Blue & Gold HMO — the approved insurance plan for the Canopy network — will have access to UCSF doctors, and vice versa.

The Canopy network currently has health providers in six Bay Area counties and intends to be in all nine in the next two years. It plans to add a second insurance provider, Western Health Advantage, in January 2018. That is expected to expand the network to 200,000 members.

Accountable care organizations are groups of hospitals and doctors that coordinate patient care and assume shared financial responsibility for that care. They essentially join many independent doctor’s offices and hospital systems as part of one large network that can more easily share records, among other benefits. The model has been on the rise since the Affordable Care Act enacted new payment incentives, rewarding providers for improving overall quality of patient care rather than what’s known as “fee for service” — paying providers for each service they order for patients.

“We all realize the days of fee for service are over,” said Dr. Todd Strumwasser, senior vice president of operations for Dignity Health Bay Area. “We’re going to be paid for providing value, which means keeping a population healthy. To do that, you have to partner with the right groups to take care of entire populations.”

The expansion of the Canopy network is part of a broader push by providers to better compete with Kaiser Permanente and Sutter Health, the two dominant health systems in the Bay Area. Kaiser, an integrated network, has about 4 million members in Northern California. Sutter and its affiliates have about 3 million Northern California patients, and recently started introducing insurance products. Canopy is far smaller.

Nationally and in California, independent providers are moving toward the integrated Kaiser model, said Dan Mendelson of the health care consulting firm Avalere Health.

“The Bay Area market is much more evolved than most areas of the country,” Mendelson said. “The strong presence of Kaiser, where you have close integration between provider and payer, means that the physicians practicing in the Bay Area are probably more accustomed to the concept of taking accountability for quality.”

Shelby Decosta, senior vice president of UCSF Health, said Canopy’s model is distinct because, unlike Kaiser and Sutter, it is a network of independent providers.

As part of the agreement, UCSF doctors will work to bring some of the health system’s programs and practices — including robotic surgery, acute rehabilitation, vascular podiatry and cardiology — to Dignity hospitals.

Formerly called the Bay Area Accountable Care Network, Canopy Health was co-founded in 2015 by UCSF and John Muir Health, which operates hospitals in Contra Costa, Alameda and Solano counties.

The 16 hospitals that are now part of Canopy are: Alameda Hospital, Highland Hospital, John Muir Medical Centers in Concord and Walnut Creek, Marin General Hospital, San Leandro Hospital, San Ramon Regional Medical Center, Sequoia Hospital, Sonoma Valley Hospital, St. Francis Memorial Hospital, St. Mary’s Medical Center, UCSF Benioff Children’s Hospitals in San Francisco and Oakland, UCSF Medical Center at Mission Bay, UCSF Medical Center at Parnassus and Washington Hospital. The network also includes three medical groups: Meritage Medical Network, Hill Physicians and Muir Medical Group IPA.