A plan by liberal think tank Center for American Progress to offer Americans a choice between Medicare or private insurance would cost $2.8 trillion over 10 years and cover 35 million people who would otherwise go uninsured, according to an outside analysis commissioned by the organization.

The analysis, by consulting firm Avalere Health, adds new depth to the Democratic debate over health care, where candidates have argued over whether to champion a single-payer "Medicare for All" system that replaces all private plans or to pursue a Medicare-like "public option" that would compete with private insurance instead.

CAP calls its own approach "Medicare Extra For All," and it ranks among the more sweeping proposals on the "public option" side of the debate. It envisions transforming Medicare into a new plan, "Medicare Extra," that would offer more generous benefits, automatically cover Americans from birth as their default option, and allow individuals and businesses to voluntarily purchase it for coverage.

The proposal is similar in structure to a bill by Reps. Rosa DeLauro, D-Conn., and Jan Schakowsky, D-Ill., although they differ on some key details. Presidential candidate Beto O'Rourke has cited the DeLauro-Schakowsky bill as a model while Joe Biden has put out a $750 billion plan that features a less far-reaching public option.

Proponents of adding a Medicare-like option argue the approach could achieve similar goals to single-payer, including near-universal coverage and lower health care costs, but without requiring new taxes on the middle class or forcing Americans to give up existing private plans.

"(The analysis) shows that universal coverage is well within reach for less than $3 trillion over 10 years and can therefore be exclusively financed through higher taxes on wealthy individuals and corporations," Topher Spiro, Vice President for Health Policy at CAP, told NBC News in an interview.

"Medicare Extra" would dramatically boost subsidies for Americans to purchase the new public plan, capping premiums at 9 percent of annual income and offering it with zero premiums and zero or minimal cost-sharing at lower incomes.

At middle and higher incomes, Medicare Extra would cover a higher percentage of average costs (80 percent) than benchmark plans do under the Affordable Care Act today (70 percent).

The Avalere study included estimated costs for alternative versions that would boost middle-income subsidies higher, which would raise the cost to $4.5 trillion at the high end. CAP also noted the Medicare Extra plan would grow significantly more expensive if it increased benefits for long-term care (an issue the Avalere study did not examine), and significantly less expensive if it restricted Medicare Extra only to individuals and families who can’t get affordable private coverage through their employer.

"Our goal here was to show an approach that has dials that can be adjusted," Spiro said.

While a majority of all Americans would be covered under the new Medicare Extra plan after a decade, the Avalere analysis also predicted that the vast majority of businesses and workers would still opt for private insurance. By 2031, 199 million people would be covered by Medicare Extra, 121 million would get insurance through their employer and 33 million would choose to remain in the Medicare program that exists today, which would be kept as an option for seniors.

The proposal would make sweeping changes to private insurance as well, however, by requiring health care providers like doctors and hospitals to charge them similar rates to the new Medicare program.

Since private insurers tend to pay providers far more than Medicare, the plan would lower premiums. But it would likely face tough opposition from various health care industry groups, who argue cuts to payments could affect their services and make it harder to attract new doctors and specialists.

The Avalere analysis did not examine potential negative consequences from the lower payments to providers, but CAP structured their plan with a goal of maintaining an average 2 percent profit margin for hospitals. The plan would boost rates for Medicaid services, which are currently lower than Medicare, and Medicare Extra plans would pay an extra 10 percent over Medicare rates for hospital care.

According to Avalere, total national health care spending — private and public — would rise initially as uninsured patients gained new access to care. But by 2031 they would come in $300 billion under current projections per year thanks to the savings from the lower rates.

The new study comes as some Democrats are warning of potential political downsides of a single-payer Medicare for All plan backed by Sens. Bernie Sanders, I-Vt., Kamala Harris, D-Calif., and Elizabeth Warren, D-Mass. Sanders has in turn argued his rivals are looking to "tinker around the edges" rather than make more sweeping changes.

On Monday, a new Marist/NPR/PBS Newshour poll found 70 percent of respondents thought a policy of "Medicare for all that want it, that is allow all Americans to choose between a national health insurance program or their own private health insurance" was a "good idea." But just 41 percent said the same of “Medicare for all, that is a national health insurance program for all Americans that replaces private health insurance."