As town and school leaders in Tisbury whittle away at the new elementary school building project, trimming costs, tweaking designs and discussing how best to manage logistics for relocating and housing students during construction, on Tuesday a new proposal came out of left field: buy the Edu Comp building to use as temporary classroom space, and later a new town hall.

Selectman James Rogers and building committee chairman Harold Chapdelaine floated the idea at a joint meeting of the selectmen and school building committee.

“Everyone knows how desperately we need space for town hall,” said Mr. Rogers, who also sits on the building committee. “We have been looking for a couple of years for a location.”

The purpose of the meeting was an update the school renovation and addition project. The building committee announced Monday that the cost of the project has been trimmed from $57 million to $53.2 million after design changes and some scaling back on size.

The architect for the project is Tappé Architects of Boston. The owners’ project manager is Richard Marks of Deadalus Projects in Boston.

The project will need approval from voters at a town meeting, with no state reimbursement money on the table this time around. A $46 million new school plan that would have come with state reimbursement was narrowly rejected by voters two years ago.

The new design retains the school’s historic 1929 exterior, with two additions, including a new gymnasium located at parking level to improve community access.

The interior of the original four-story brick school will be completely renovated, with both traditional classrooms and multipurpose spaces including library areas on every floor. Skylights and glass walls will distribute natural light throughout the building, which will be powered by electricity and have the capacity to become energy-neutral.

Photovoltaic roof panels are part of the design, but the $1.6 million cost is not included in the budget.

“There are many ways to finance that, and we’ll be exploring them with the town,” Mr. Marks said Tuesday. “It’s very doable.”

Building committee members are unified in support of the new design, Mr. Chapdelaine said, but the process took weeks of occasionally contentious negotiations.

“There has been plenty of disagreement . . . and coming to consensus,” he said.

But before asking voters to borrow more than $50 million for the project, the town needs to decide where learning would take place while the project is underway.

“There’s no way to keep the children and staff safely in the building during this much construction,” Mr. Marks said.“We may get [construction] down to a year and a half, but it’s really going to be two academic years that are going to be affected.”

The project currently budgets $2.5 million for temporary classrooms, about half the amount needed to house all the grades. At a building committee meeting Monday, Mr. Marks recommended finding existing locations in town for the youngest and oldest students — a prospect that worried some committee members, who have already seen the school divided when asbestos and lead remediation work forced its middle-school grades to share the high school campus in Oak Bluffs a year ago this fall.

On Tuesday, Mr. Chapdelaine and Mr. Rogers, who also chairs the select board, advanced a new proposal, saying Tisbury should explore purchasing the Edu Comp building, to use first as a temporary school and then as the next town hall.

The owners of Edu Comp announced early this month that they would close the store and put the building, which sits at the head of Main street, on the market.

The building alone is too small for the entire school population, but Mr. Rogers said it has a large parking lot and sits at the edge of town-owned Veterans Memorial Park, which already was a proposed location for temporary classrooms.

“The entire student body would be approximately on the same location,” he said. “They have a playground they can use. It’s really a win-win—a win-win-win, really.”

As of Tuesday evening, no direct contact had yet been established with the building’s owners, Dorothy Gregory and Shannon and Dan Carbon.

“Phone calls have been made,” selectman Jeff Kristal said.

Mansion House Hotel co-owner Josh Goldstein, who attended the meeting, backed the idea enthusiastically.

“Pat Gregory would have loved this,” Mr. Goldstein said, referring to the late founder of Edu Comp.

“Pat was an educator to his core,” Mr. Goldstein continued. “As an abutter, I fully support this project and Mansion House stands by to help the town any way we can.”

The Mansion House is a direct abutter to Edu Comp.

Selectmen said they would put the matter on the agenda for the board meeting Tuesday.