Michael Bloomberg, who is seeking the Democratic presidential nomination and has been positioning himself as a moderate in the race, proposed forgiving the college debt of some borrowers on Monday, but on a far more limited basis than either Senator Bernie Sanders or Senator Elizabeth Warren.

Believing other plans are too expensive and would cancel the debt of some borrowers who don’t really need it, Bloomberg would limit forgiveness to those who went to failed or predatory for-profit colleges and those who have made decades of payments on income-driven repayment plans.

“People are burdened with debt for decades and we need to put a stop to it,” Gina Raimondo, the Democratic governor of Rhode Island, said during a call with reporters. Raimondo, who endorsed Bloomberg’s plan, said her state’s own free community college program has led to the highest enrollment at two-year schools in the state’s history and tripled enrollment by people of color.

Unveiling his higher education plan Monday, Bloomberg joined other Democratic candidates in proposing to make community colleges tuition-free. He would also make four-year colleges free. But unlike Sanders and Warren, his plan only would do so for the lowest-income students, whose families make less than $30,000 a year on average.

In contrast, Joe Biden and Senator Amy Klobuchar would only make community colleges free. Bloomberg’s plan also would be more limited than former South Bend, Ind., mayor Pete Buttigieg’s proposal, which would make public colleges tuition-free for families who earn up to $100,000. Students from families earning $100,000 to $150,000 per year would get tuition subsidies on a sliding scale under Buttigieg’s plan.

Bloomberg’s plan, estimated to cost $700 billion over 10 years, calls for doubling the maximum Pell Grant to $12,690. It would also create a two-for-one federal matching program for states and institutions committed to keeping increases in the full cost of attending college from rising above the inflation rate.

To lower loan payments, Bloomberg also said he’d enroll current and future undergraduate borrowers in income-driven repayment programs that would be capped at 5 percent of discretionary income, down from the current 10 percent rates. The income-based plans also would forgive up to $57,000 of borrowers’ loans if they make reasonable progress in repaying loans for 20 years.

Saying only 7 percent of students at highly competitive colleges and universities come from low-income families, Bloomberg would require institutions that receive federal aid make public their admission rates for legacy and nonlegacy candidates. If progress isn’t made toward ending legacy preferences, he’d consider limiting federal funding to the schools.