In Bridgewater, developers have proposed at least four residential projects under the state law that allows them wide latitude to build high-density housing in communities that lack sufficient affordable units.

In Marshfield, two projects are in the works under this statute, known as Chapter 40B, and Walpole is beginning to wrestle with a proposal for 250 condominiums. Pembroke is doing the same after receiving a pitch for 68 condo units earlier this year, to the dismay of selectmen.

But the story is different in Quincy, where officials recently turned away a 40B project they viewed unfavorably. They could do that because they say the city has met one of the state’s affordable-housing thresholds, which include having at least 10 percent of its housing used for affordable units or 1.5 percent of its buildable land used for that purpose.

Hitting at least one of those thresholds -- and getting out from under the yoke of Chapter 40B -- is a primary goal now for many cities and towns as they grapple with escalating demand for housing and developers eager to capitalize by putting up large-scale or high-density projects.

In communities not exempt from 40B, builders are not subject to most zoning bylaws and restrictions other developers would face, as long as they set aside a quarter of their units at affordable rates for households earning no more than 80 percent of the area’s median income.

In Bridgewater, town officials are working to pass an inclusionary zoning bylaw requiring developers building projects of a certain size to include a percentage of affordable units, or to make a donation to an affordable-housing trust, said Andrew DeIonno, director of community and economic development.

The aim is to get to one of the 40B thresholds -- and exempt status from the law -- as soon as possible.

“We have 40B communities smack in the middle of industrial areas, which the state has found acceptable,’’ DeIonno said. “I don’t find that acceptable.’’

The town has worked to clean up its zoning, but 40B projects can still be placed in areas that aren’t zoned residential, he said. “That’s why it’s important for us to get control of our destiny.’’

But some municipalities have run into obstacles as they try to build more affordable housing.

In Marshfield, for example, there isn’t a lot of suitable land outside the local flood zone, which according to the latest Federal Emergency Management Agency maps covers a third of the town, said town planner Greg Guimond. “We have these limitations we’re trying to work through,’’ he said.

Six percent of the housing stock in Marshfield is affordable, and if two 40B projects in planning stages are completed, that figure would rise to 8 percent, Guimond said. The town’s efforts in the past have been to donate land for affordable housing or to help people trying to buy a home in town, but adding only four or five affordable units a year means taking a long time to reach the thresholds, he said. The town is looking for more sites to build on, he said.

The Zoning Board of Appeals in recent months has reviewed the pair of 40B projects, including a 270-unit plan with 68 affordable units called Modera Marshfield, believed to be the town’s largest 40B proposal to date.

Rather than aggressively asserting its position using the law, the developer, Mill Creek Residential, has worked to engage the town from the beginning, trying to dissuade officials from putting too many conditions on the project, said Lars Unhjem, the company’s vice president of development. Local officials can impose conditions that can make some projects unviable, which then have to be dealt with in an appeals process, he said.

“We don’t view it as a sledgehammer,’’ Unhjem said of the 40B law. “It definitely helps us find opportunities where otherwise there would be none.’’

Housing advocates agree, and they applaud sensible use of the statute to create more housing for lower-income families.

Carl Nagy-Koechlin, executive director of Housing Solutions of Southeastern Massachusetts, which works with families seeking affordable housing, said there is high demand for 40B housing, and lotteries draw many would-be buyers or renters.

The law allows higher-density housing in towns that otherwise wouldn’t allow it, and creates housing stock at price points that wouldn’t be built otherwise, Nagy-Koechlin said.

“That’s why 40B is such a valuable tool,’’ he said. “It’s the only way you can get anything done.’’

But the statute is also viewed with disdain by many who fear the impact of dense subdivisions.

In Walpole, the Board of Selectmen is redoubling its efforts to increase the town’s affordable-housing stock from about 5 percent to 10 percent, to avoid plans like the one it recently received from Pulte Homes for 250 units at the Walpole Woodworkers site on East Street.

Selectwoman Ann Ragosta said she is concerned that there are many new homes being built in Walpole but that not many are affordable, making it harder to hit the state thresholds.

“How are we in the process of constructing almost 600 units, and only 40 of the units are affordable?’’ Ragosta asked during a recent board meeting.

Board chairman Eric Kraus said in an interview that the town is concerned about the size of the Pulte Homes proposal, not that it’s a 40B development.

The project is in the very early stages, and the town is communicating its concerns about parking, traffic, safety, impact to the school district, and strain on the water and sewer systems to MassHousing, an agency working with the developer, Kraus said.

The town must “start being overly aggressive in managing this, instead of reactive,’’ he said during the meeting.

Like Walpole, Quincy has many new market-rate housing units coming online, but it has long had an affordable-housing trust and an inclusionary zoning law, both of which have encouraged the development of housing for people with low and moderate incomes, said community development director Sean Glennon.

The city is just shy of the 10-percent affordable threshold, at 9.6 percent, but meets another 40B benchmark of having at least 1.5 percent of its buildable land used for affordable housing, Glennon said. As of March 2014, the city’s land use for affordable housing is 3.26 percent. Recently, it denied a 40B project of more than 30 rental units.

“Your best defense against bad 40B projects is to get your affordable housing up to 10 percent,’’ said Nagy-Koechlin.

Jill Terreri Ramos can be reached at jill.ramos@globe.com.i.