WASHINGTON — Six million more Americans could soon benefit from the government’s most generous student loan repayment plan as the Obama administration expands a program that has become a cornerstone of the president’s education policy.

The repayment program, known as Pay as You Earn or PAYE, caps borrowers’ monthly bills to 10 percent of their income and forgives the debt after 20 years of payment.

So far, it’s only been available to people with especially low income relative to their debt and who took out their loans after 2007.

The administration, however, is proposing to expand the program to anyone with an existing federal loan, regardless of their income.

The Education Department, which is accepting public comment on the proposal, expects to finalize the rule in late October. The changes will only apply to existing student debt since it would take an act of Congress to cover new loans.

But letting more people peg their monthly loan payments to a small share of their income will mean raising the cost of an already expensive program.

A copy of the proposal published in the Federal Register Thursday said it will cost $15.3 billion over 10 years, nearly doubling the program’s current cost. Congressional Republicans have already criticized the rising cost of the administration’s loan repayment plans.

Still, the government’s flexible repayment plans are critical as student debt tops $1.3 trillion and people struggle to find jobs that pay enough to cover their monthly loan payments.

Income-driven plans are designed to prevent borrowers from defaulting on their loans, a problem faced by about 20 percent of people repaying college debt. Defaulting on student debt can severely damage a person’s credit rating, making it much harder to buy a car or a house.

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