The Boston Licensing Board could decide Thursday whether to grant a full liquor license to Dot 2 Dot Cafe, a Dorchester Avenue restaurant that doubles as a meeting space for local residents and organizations, and which is the place City Councilor Ayanna Pressley says she had in mind when she led a successful effort to gain more liquor licenses for the city's outer neighborhoods.

Pressley, former state Rep. Mel King of the South End and several Dorchester residents attended a board hearing Wednesday to voice support, saying the struggling restaurant has helped turn around the St. Mark's area of Dorchester Avenue, goes out of its way to help local organizations and artists and needs the boost it would get from liquor sales to stay afloat and expand.

Co-owner Karen Henry-Garrett, a graduate of Cordon Bleu in London, said a liquor license would enable her to serve dinner on a regular basis at the 1739 Dorchester Avenue restaurant; it's just not financially possible to do so on a regular basis without the additional revenue that would come from drinks, she said.

However, Board Chairwoman Nicole Murati Ferrer said the board might have to defer any vote because of issues related to legal issues surrounding the limited liability corporation Henry-Garrett and her husband Richard Garrett set up to oversee the restaurant. Although the Garretts are the owners, both are British citizens, so they enlisted three American residents from Dorchester as board members to meet legal requirements for LLCs.

That might satisfy the state and the IRS, but state liquor regulations require statements on how much of the LLC's profits each board member would get, Ferrer said.

Henry-Garrett said she hadn't thought that far ahead, because the restaurant has yet to actually turn a profit.

Tom McDonough, aide to at-large City Councilor Steve Murphy, jumped in and volunteered to help the Garretts wade their way through the legalities of Massachusetts liquor laws. McDonough was one of several people who spoke strongly in favor of the application - and who urged board members to try the cafe's food. He said he and his wife are "big fans" of brunch there.

Pressley, an at-large councilor who lives in Dorchester, said Dot 2 Dot Cafe is the very profile of "a business providing a public good," and exactly the place she said she thought of when she began a campaign to bring more liquor licenses to neighborhoods such as Dorchester and Roxbury, because of the positive impact the cafe has had on the surrounding area. Henry-Garrett "has been an incredible and philanthropic partner" with residents working to improve the area, she said.

Under a law passed earlier this year, Boston will get 75 new liquor licenses over the next three years, to be doled out in specific neighborhoods - and which cannot then be transferred out of those neighborhoods.

Nearby resident Beth Parkhurst said her knitting group regularly meets at the cafe and said it perfectly fits the multi-cultural vibe of the neighborhood. "Karen is British, but she puts up decorations for St. Patrick's Day," she joked. "You can't get more multi-cultural than that." She added that Henry-Garrett is "an outstanding chef," whose "cooking is worthy of a top downtown restaurant, but it's at neighborhood prices."

King told the board he makes regular trips to the cafe from his home in the South End - and that he always tries to bring people with him to introduce them to it. "It's an atmosphere you will not see anywhere else," he said, urging the board to do whatever it can to help it out.

Also Thursday, the board could decide whether to grant a full liquor license to Pho Le, 1356 Dorchester Ave., also from the set of new licenses the city now has.

Pressley also supported this application, saying the Vietnamese restaurant is an example of the diversity of food options in Dorchester, something she said the city should support.