The proposed $84.8 million renovation of Blue Hills Regional Technical High School now has the support of five of the district’s nine member municipalities, but the rest have yet to act as the deadline nears.

James P. Quaglia, superintendent-director of the school, said the nine were asked to give their endorsements by Nov. 18 for the project, the first major one since the 51-year-old school built an addition in 1976.

If any of the nine don’t back the plan, the school has the option of holding a districtwide vote, though Quaglia said he is hoping that all members give the go-ahead.

“We really wanted to plead our case to them and have them support it one at a time,’’ he said, adding it would be better for maintaining relations with the member towns than going directly to voters.

The school, at 800 Randolph St. in Canton with a picturesque view of the Blue Hills behind, enrolls students from Avon, Braintree, Canton, Dedham, Holbrook, Milton, Norwood, Randolph, and Westwood. It was formed in December 1963 by seven of the towns. Dedham and Milton joined in 1987, as demand by area residents and employers for vocational and technical education continued to grow.

So far, Quaglia said, Avon, Braintree, Canton, Milton, and Randolph have indicated support for the project by a vote of town councilors or Town Meeting, or by not taking any action to oppose it, which allows the plan to move forward.

Norwood will be taking it up at its Special Town Meeting on Nov. 6, with the final three towns scheduled to act on Nov. 13.

In one of the three, Holbrook, taxpayers are just beginning to pay for a local K-12 school that opened in September, and they may find an additional expense for schools an unacceptable burden.

“I think most people recognize the value of the project, but the timing of it is very challenging for the people of Holbrook,’’ said Holbrook Town Administrator Timothy J. Gordon of the Blue Hills request.

The cost of the town’s K-12 school is adding about $650 annually to the average taxpayer’s bill.

Gordon said the Blue Hills project would add $300,000 to the $1.8 million Holbrook pays each year from its operating budget for sending 129 students to the regional school.

The project has been in the works for six years, as Blue Hills sought reimbursement approval from the state.

The Massachusetts School Building Authority agreed in August to reimburse 55.89 percent of the project, with the member municipalities paying the remainder, with a share determined by the average number of students they send to the school.

For example, students from Randolph make up about 30 percent of the 862-student population, Quaglia said, so that town would pay slightly less than one-third of the project cost. Westwood sends the fewest students.

Though Randolph has indicated support for the proposed renovations, the decision was not a unanimous one.

Arthur Goldstein, vice chairman of the Randolph Town Council and the head of its finance subcommittee, voted no, saying it is too much money for Randolph to pay when it’s struggling to support schools within the town that serve more students.

He said the Town Council gave the local School Department only $1 million of a $1.5 million increase request last year. The town spends $21,000 per Blue Hills student, while spending $16,500 per student in Randolph schools, said Goldstein, a certified public accountant.

Also, he said, the renovations would not add any educational space at Blue Hills.

The project calls for new heating, electrical, and plumbing systems; security and public safety systems; new windows and athletic lockers; and improvements to the roof. Plans also call for the building to be made more accommodating to those with disabilities.

If approved, Quaglia said the work could begin at the end of June and continue into the following summer, with work during the school year being done primarily on the second and third shifts. Some summer activities would be relocated or canceled.

He said the property doesn’t lend itself to constructing a separate building on the site, and the existing building, though in need of repair, is not in such poor condition that it should be razed.

“The bones of the building itself are good, and the building is worth saving,’’ he said.

Jean Lang can be reached at jeanmcmillanlang@gmail. com.