For thousands of Philadelphia homeowners whose property assessments — and tax bills — will more than double next year, relief could be on the way with a new proposal from City Council President Darrell L. Clarke.

Clarke, along with Council Members Kenyatta Johnson, Mark Squilla, and Maria Quiñones-Sánchez, introduced legislation Thursday that would lower the threshold at which homeowners qualify for a key property-tax relief program. The Longtime Owner Occupants Program (LOOP) began in 2014, when the city started assessing properties at 100 percent of market value, or the amount for which they could be sold. Currently, homeowners qualify if their assessment increases 200 percent or more in one year; Clarke would lower that threshold to 50 percent.

Aimed to assist longtime residents of gentrifying neighborhoods, the program freezes assessments used to calculate tax bills. Expanding it could bring relief to about 3,000 additional households, said Jane Roh, a spokesperson for Clarke.

The proposal comes after the city assigned new values to every residential property this year for the first time since 2014. The changes sparked outrage from residents as well as Council members, who did not pass Mayor Kenney’s proposed tax increase and have commissioned an audit of the Office of Property Assessment.

The median value of a single-family home increased 10.5 percent citywide, and nearly 12,000 assessments increased more than 100 percent, according to an Inquirer and Daily News analysis.

In Johnson’s district, 472 additional homeowners could potentially qualify under the lower threshold, according to an analysis by Clarke’s office. “You can imagine the latest LOOP amendment would open the program up to a lot of residents facing tax hardships who are just barely ineligible,” Johnson said in a news release.

Homeowners qualify for the program if the property has been their primary residences for at least 10 years and they meet certain income requirements. A single person must earn less than $91,800 per year to qualify, for example, and a four-person household must have an annual income of less than $131,000.

Clarke’s office analyzed the most recent assessments and found that about 75 percent of households that had assessment increases between 50 percent and 200 percent are in census tracts with low to moderate income, meaning their income levels would likely qualify.

Lowering the threshold of assessment increase required to qualify would cost less than $1.5 million in tax revenue for the city, Roh said.

“In other words, the city can certainly afford to lower the threshold, and doing so will save taxpayers money in the long run,” Roh said in an email, noting that dealing with homeowner displacement and homelessness also costs the city money.

“We look forward to reviewing the proposal and working with Council members on this important matter,” Mike Dunn, a spokesperson for Kenney, said Thursday.

More than 16,000 homeowners are already enrolled in LOOP, according to the city. Officials said that number represents about three-fourths of the households that are eligible to participate.

Philadelphia also offers a small tax break for owner-occupied homes, tax freezes for low-income seniors, and installment payment plans. But beyond those programs, there is no limit to how much assessments or tax bills can increase in a given year. The city and School District expect to receive an additional $85 million in revenue in the current fiscal year from assessment increases alone.

The audit of the Office of Property Assessment, which Clarke has said he hopes will lead to improvements in the city’s methods of valuing properties, was expected to be made public this fall but is still under review.

This article has been updated to correct percentages for the current assessment increase required to qualify for LOOP, as well as the percentage increase that would qualify residents under the proposed legislation. City officials previously provided the Inquirer with incorrect figures.