State Treasurer Steven Grossman, who chairs the agency, called it “a great day” for Plymouth and its students.

“We can now partner with the district on possible solutions to the deficiencies that have been identified at the high school,” Grossman said.

During the 270-day eligibility period, the building authority determines the readiness of the community and school district to enter into the capital spending pipeline. The agency also expects the school district to establish a school building team.

Plymouth already meets the financial commitment requirement, having approved funding for the project in 2006, when voters authorized a $199 million tax increase to pay to upgrade both of its high schools and to build a senior center.

The new Plymouth North High School has just been completed and will be ready to open this fall. Senior center construction is also well underway.

While Plymouth South High School is just 25 years old, the town’s population has outstripped its size, a concern to the district’s administrators.

The next step will be for the building authority to authorize a feasibility study to determine how to address shortcomings at the school. The study could recommend a renovation and expansion or a new school building.

State Senate President Therese Murray, Democrat of Plymouth, said she is happy the town has been invited to complete the eligibility phase for Plymouth South.

“The construction of the New Plymouth North was a great success, and these improvements to our high schools will help ensure that our students receive a high-quality education with the best facilities and resources,” she said.