A local couple’s hopes of building a house on a sprawling beachfront parcel on Plum Island have been delayed, perhaps permanently, after a neighbor objected to their plans.

Sandy Lepore, whose property abuts the 5.4-acre undeveloped lot on Temple Boulevard, last Thursday asked the state Department of Environmental Protection to issue a superseding order of conditions for the project proposed by Ralph and Betsy Cox.

In her 48-page request, submitted to the state agency on the last day that such an appeal could be filed, Lepore said “the project does not meet the applicable performance standards for work within coastal dunes and a barrier beach, and, accordingly, it should be denied.”

The appeal will be reviewed by the DEP’s northeast regional office, according to Ed Coletta, spokesman for the state agency.

“One of our staffers will review the case itself, set up a site visit, and probably bring in all sides in the case to explain their thoughts,” said Coletta. “Then, they will request any other documents they think they need or any other information that was mentioned at the site visit. They’ll review all of that information and make a superseding order, either reaffirming the local order, perhaps with additional conditions, or overturning the local decision.”

The process, Coletta said, is likely to take several months.

The case could drag on even longer, he noted, should any party aggrieved by the decision of the Northeast office decide to file an appeal with the Boston office. Any decision issued by the Boston office could also be appealed in state superior court, Coletta said.

For now, though, all eyes are on the appeals process, which will consider the May 3 decision of the Newbury Conservation Commission. The seven-member body approved plans presented by the Coxes, who live in Newbury, less than a mile from the vacant lot. The couple had requested permission to build a pile-supported, single-family home with a clamshell driveway and walkways to the Atlantic Ocean.

The Coxes did not respond to a voice-mail message left at their home Monday seeking comment.

In documents submitted to the Conservation Commission on their behalf, Tom Hughes, the couple’s environmental consultant, said the project would “result in a healthier dune system,” noting that portions of the undeveloped lot have been disturbed by both people and pets, and as a result, “there are areas where foot traffic and fires have devegetated portions of the primary dune, causing erosion . . .”

According to the notice of intent prepared by Hughes Environmental Consulting, the Coxes would remove debris piles from the site and take pains to “relocate and replant all native plants within the project’s limit of work.”

Those assurances failed to appease neighboring property owners, 13 of whom together submitted to the commission a list of concerns regarding the project’s impact on “protected open space designation, storm damage prevention, flood control, and the protection of wildlife habitat.” The Plum Island homeowners said they feared the construction would adversely affect local wildlife and damage the foundations of nearby homes.

A letter drafted by Lepore’s environmental consultant, LEC Environmental Consultants, Inc., noted that the dunes of the barrier beach are “significant to storm damage prevention and flood control” and questioned whether the impact of the 3,200 square feet of shading from the house and its decks could destabilize the dune.

The property, bounded by Temple Boulevard to the north, the Atlantic Ocean to the east, the Parker River Wildlife Refuge to the south, and Sunset Drive to the west, is considered the largest beachfront parcel on Plum Island. The parcel includes primary and coastal dunes and wetlands.

The land, made up of “remainder lots’’ from an early-20th-century cottage-lot subdivision, was conveyed to the town several decades ago. In 2010, Town Meeting voters authorized the selectmen to sell the parcel. The Coxes have submitted an offer to buy it for $550,000. That offer is contingent on the couple’s successful permitting of their construction plans. If the deal is finalized, the proceeds would be used for capital improvements.

The sale comes at a crucial time for the town, which is facing financial hardship.

For the second consecutive year, a tax hike that local leaders had said was critical for Newbury’s fiscal health failed at the ballot box. The May 8 vote was 616 in favor of and 667 against a $293,000 override, or permanent property tax increase.

Last spring, a proposed override of $950,000 failed by 200 votes.

Neighbors are hopeful that, ultimately, the fate of the Temple Boulevard parcel will not be influenced by Newbury’s budget woes, but “decided on the science and the law,” Lepore said.