Eight bills that would allow individual municipalities to add a new fee to certain real estate transactions advanced from one legislative committee, while another is taking more time to decide on a proposal that would allow cities and towns to take such a step without first getting Beacon Hill’s approval.

As of Wednesday’s deadline for most committees to act on bills, the Housing Committee had put forward an order extending until May 9 its window to advance or reject legislation that would enable municipalities to impose a fee of between 0.5 percent and 2 percent of the price of certain housing transactions in order to generate revenue to preserve affordable housing and fund new home construction.

The fee rate and any exemptions would be set locally, and the bills (H.1377, S.868) call for the new fees to be applied only on transactions featuring prices that are above the statewide or county median single-family home price.

While the decision could bottle the bills up for three more months, Rep. Mike Connolly, who filed the House version and serves on the Housing Committee, said he viewed the extension as an “encouraging sign.”

“I’m grateful that we have the opportunity to continue the conversation and look to build consensus around it,” he said.

Connolly, a Cambridge Democrat, said he sees momentum gathering behind the idea of transfer fees, with Boston Mayor Michelle Wu this week filing a home-rule petition that would allow her city to impose a fee on sales of $2 million or more and major employer Mass General Brigham earlier this month voicing support for the bills filed by Connolly and Sen. Jo Comerford.

“I think the momentum is a product of the ongoing affordable housing emergency, and I’m cognizant of sort of the unique trajectory of this legislative session,” Connolly told the News Service. “When the legislative session started, the real housing advocacy focus was on stopping evictions and foreclosures, in a way where those immediate COVID housing concerns were really dominating a lot of our bandwidth and our advocacy attention.”

A little more than a year into the two-year session, Connolly said there’s now “a chance to focus more on the regular agenda,” though pandemic response activity continues.

“Those underlying issues of housing costs haven’t gone away,” he said.

High costs in Massachusetts can burden renters and present a barrier to homeownership for many.

Amid a lack of housing inventory, the state’s median home sale price in 2021 surpassed $500,000, The Warren Group, publisher of Banker & Tradesman, reported Tuesday. The new annual median of $510,000 represents an increase of more than 14 percent from 2020.

The Connolly/Comerford bills are backed by a collection of community organizations, planning agencies and other groups, the Local Option for Housing Affordability coalition, which also supports a handful of bills filed by individual municipalities where local officials have already backed proposed transfer fees.

“We look forward to continuing to work with the legislature on this extremely important issue. It is a vital measure to have enacted this session for communities from Nantucket, to Boston, to Western Massachusetts,” Nantucket housing director Tucker Holland said in a statement offered by the coalition.

Bills proposing transfer fees in Somerville (H.3938), Provincetown (H.3966), Concord (S.2437), Boston (H.2942), Arlington (H.4295), Cambridge (H.4282), Nantucket (H.4201) and Chatham (H.4060) all earned favorable reports from the Revenue Committee, moving them along them in the legislative process.

A favorable report doesn’t guarantee a bill will pass, or even make it to the floor for a vote. Similarly, the Housing Committee’s extension order doesn’t carve May 9 in stone as a final deadline for action on its bills, as committees can seek further extensions and lawmakers may opt to advance policies as attachments to other vehicles including the annual state budget.