A Small Business Administration spokesman said the agency was “committed to ensuring that the next round of P.P.P. is launched as quickly as possible.”

According to outlines of the bill circulating among congressional officials on Monday, hotels and food-service businesses would be eligible for bigger loans this time, up to 3.5 times their average monthly payroll. Other borrowers would again be limited to 2.5 times their payroll.

Publicly traded companies would be ineligible for the new loans, eliminating a provision that provoked a public outcry as deep-pocketed restaurant chains, software companies and drug makers, among others, collected taxpayer-funded loans.

The new bill would also expand the list of expenses that a loan could be used to pay, which previously were limited mostly to payroll, rent and utilities. Businesses could now use the money to buy supplies from their vendors, buy protective equipment for their staff or fix property damage “due to public disturbances,” according to a House Small Business Committee summary — a reference to this year’s protests over police brutality and systematic racism.

But the biggest change would reopen the program to some businesses that had already received help.

When the Paycheck Protection Program expired in August, about $138 billion had not been spent. Many business owners who had received money said they would gladly take another loan, but the program’s rules prevented them from getting a second helping. The new relief bill offers a second cash infusion for those who meet stricter terms: Borrowers with fewer than 300 employees that had a 25 percent drop in sales from a year earlier in at least one quarter could qualify for an additional loan of up to $2 million.

“We are absolutely applying,” said Dana Sanford, the office manager for A&J Transportation, a trucking company in Oklahoma. A&J recently completed the process of having its initial $699,000 loan in the program forgiven, which Ms. Sanford said had gone smoothly.

“I am very excited about the second round of P.P.P.,” she said. “It really helps the businesses pay their people.”