Elected officials are lobbying the state to expand the scope of its long-promised South Coast commuter rail project by adding a spur leading to the mouth of the Cape Cod Canal.

The push comes after state transportation officials in June announced they may change the route for the South Coast project to save time and money. The adjusted route, currently being studied by the Massachusetts Bay Transportation Authority, would send trains farther east and closer to Cape Cod on their way to New Bedford and Fall River.

Politicians and business leaders in the canal area say that if the new route were to be adopted, it could set the stage for transit stops in Bourne and Wareham.

The proposed route would not be a direct shot from South Station in Boston. Instead, when the South Coast train stops in Middleborough, travelers headed to Cape Cod could switch to a “shuttle’’ train that would take them to the Bourne village of Buzzards Bay, on existing tracks used by the CapeFlyer, a train that runs on weekends in the summer.

The idea may be something of a wish-list item. MBTA spokesman Jason Johnson said the state is not currently considering expanding the South Coast rail project to include a shuttle train to the Cape.

Advocates, however, say the trip would attract riders who would otherwise be stuck in Boston traffic.

“It’s not just for commuters. It’s everything Boston has to offer,’’ said Republican state Representative Susan Gifford of Wareham. “There are a lot of people down here who see doctors up in Boston. Parking and traffic can be a nightmare.’’

While the state operates the weekend CapeFlyer service, there has not been daily year-round service between the city and the peninsula since 1959.

That’s not for lack of trying. In 2015, Bourne voters chose to join the MBTA’s service area, which involves paying the agency an annual fee, in hopes that doing so would be the first step toward bringing commuter rail to Buzzards Bay. In April, however, a proposed pilot service was all but rejected by the MBTA’s governing board, due to cost concerns.

But since June, when transportation officials announced the possible South Coast rail rerouting, which would send trains through Middleborough instead of Stoughton, state representatives, town governments, and business leaders on and near the Cape have felt emboldened to keep pressing. Middleborough, they reasoned, is already a stop on the CapeFlyer route.

Supporters of the Buzzards Bay proposal see a political reason to tie the idea to South Coast rail, too: It could win public support for the broader project, for which Governor Charlie Baker voiced support during his 2014 campaign, because more municipalities would benefit.

“It’s a great opportunity for South Coast Rail to pick up more partners and allies . . . in this whole area of southern Plymouth County and the Upper Cape,’’ said Representative William Straus, Democrat of Mattapoisett. “If I was the governor I’d say: ‘Wow, I got [Fall River and New Bedford] done but I also got Cape Cod done, too.’’’

Straus’s backing is a key development for supporters. The Democrat cochairs the Legislature’s Transportation Committee, and has been working with Gifford and Bourne Representative David Vieira, another Republican, to call on the state to further investigate rail service to Buzzards Bay.

Advocates say that rerouting the South Coast project through Middleborough would be cheaper than the proposed route through Stoughton, which is projected to cost $3.4 billion. The savings, they argue, could be reinvested in a spur toward the Cape.

But Paul Regan, executive director of the MBTA Advisory Board, which represents cities and towns served by the transit authority, was more skeptical. Under the Baker administration, the T has largely focused on reining in costs and emphasizing improvements to existing service over expanding the system, he said.

“Is it feasible? Sure,’’ he said. “But I have no idea how this gets paid for.’’

Adam Vaccaro can be reached at adam.vaccaro@globe.com. Follow him on Twitter at @adamtvaccaro.