“West Tisbury is a hungry town,” Toni M. Cohen said Wednesday as she looked across a packed meeting room where popular Island restaurateurs Mary and Jackson Kenworth were seeking approval to demolish, rebuild and enlarge the burned-out Deon’s restaurant on State Road.

Most of those attending, including residents and town officials, voiced support for the Kenworths’ new restaurant plan, but the zoning board of appeals was uncertain whether the proposal is allowed under zoning regulations.

Ms. Cohen and her fellow board of appeals members spent one and a half hours searching for solutions before continuing the hearing until July 17 at 6 p.m. in the town hall.

Zoning regulations prohibit commercial buildings of more than 2,000 square feet in residential neighborhoods. The Kenworths — who have operated the Slice of Life restaurant on Circuit avenue in Oak Bluffs since 2003 and who founded Sweet Life Cafe on Circuit avenue in 1996 before selling it a year ago — want to demolish the 2,154 square foot building and replace it with a 2,560 square foot restaurant on the two-acre site they have an agreement to purchase.

The lot contains both the restaurant and a four-bedroom house and is owned by Pebco LLC. While pre-existing nonconforming footprints have been approved in the past, the issue for zoning board is whether demolishing the structure subjects the new structure to the 2,000-square-foot size limit for new buildings.

“I believe we have the power to alter or extend a pre-existing, nonconforming property like this but I question whether we have the ability under zoning regulations to approve demolishing and rebuilding on a footprint larger than 2,000 square feet,” board member Anthony Higgins Jr. told the applicants.

“We’re going round and round right now. There is a legal issue here,” said board chairman Eric Whitman before continuing the public hearing for three weeks to allow the board to consult with town counsel.

“Based on the public support you’ve received, I don’t think there is an approval problem . . . but I don’t think we have the power to grant a special permit based on this plan,” Mr. Whitman told the Kenworths.

The proposed and yet-unnamed restaurant drew 20 letters of support and a dozen positive comments from 25 to 30 residents at the hearing. Several abutters, including the original owner of the site, called for a reduction in late evening noise from exiting diners.

Abutter William Haynes said, “I built the building so I can’t be totally against [the plan] but I abut on three sides. You’ve got to make sure parking is increased and noise is reduced. We are here at home at 10 at night when the place closes and customers are saying good night and slamming car doors.”

Kathleen Kaempfert, owner of the The Farmhouse bed and breakfast next door, catalogued a history of noise and parking encroachments on her property. “I am a supporter I guess, but I have guests who want to sleep at 10 o’clock at night,” she said.

Some board members suggested the building could be moved closer to the road, but architect Chuck Sullivan said the current plan meets 50-foot setback rules.

Mary Kenworth said abutters to the Sweet Life included the Camp Ground and the relationship had been complaint free.

The Kenworths said their design will move things inside the restaurant that have been outside and a source of noise problems in the past, including some mechanical systems. The restaurant plan calls for an inside waiting area that also would serve as cafe seating for up to 12 people in the summer and during winter months.

The plan for an inside waiting area for diners and moving all parking to the rear of the restaurant is a response to noise and parking concerns. Parking would expand from 16 to 22 vehicles and seating capacity would increase from 44 to 60.

Residents praised the Kenworths’ culinary skills and the prospect of a 10-month restaurant in town.

“I’ve been going there since it was Fat Tony’s,” said resident Don Ogilvie. “I understand there are problems to work through. [The Kenworths] are famous on the Island for their restaurants. Don’t turn them down because they’ve tried to do the right thing,” he told the board.

John Hoff, owner of nearby Middletown Nursery, said: “How brave of these people, with their tremendous track record, to try this. I want to give them support and I think we ought to give them the benefit of the doubt.”

Norman Hall said: “West Tisbury residents are going to be the major users of this place. Many of us can bike or even walk. These are great people, they know what they’re doing. Nothing else is going to come in here.”

Begun in the 1950s as a takeout ice cream shop, the building has had eight to ten names and operators and has expanded in size. Health agent John Powers said the septic system can accommodate 60 diners.

Mrs. Kenworth said chronic turnover at the site is a result of size restrictions. “I don’t think you’re going to find anyone else willing to do this,” she said.

“Our business plan is very specific and detailed. We have pushed this to the [financial] limit.”