The corner store could become a thing of the past if members of the new liberal group Cambridge Citizens for Liveable Neighborhoods (CCLN) have their way.

Although the Cambridge Board of Zoning Appeals currently has the authority to grant variances that allow business to set up shop in residential neighborhoods, CCLN has submitted a petition to the Planning Board that would change Cambridge's zoning ordinance so that no such variances could be granted there.

In the petition, filed with the city on April 6, the organization writes that "variances to the zoning ordinance have become too commonplace and too easy to obtain" and asks the City Council to amend the ordinance to limit the power of the Zoning Board.

"The Board of Zoning Appeals takes a `Sure, why not?' approach to anyone's application [for a variance]," said R. Philip Dowds, a member of the steering committee of CCLN. "Amending the ordinance eliminates ambiguity and says to the Zoning Board that they can't do that anymore."

Under the proposal, citizens or developers wanting to open a business in a residentially zoned or open space area would be forced to request that the council rewrite the zoning ordinance or change zoning lines, said CCLN co-chair Daniel E. Geer.

"There will still be lots of ways that commercial uses can be put in residential districts," Dowds said. "It just won't happen that the Zoning Board of Appeals will have all the say-so."

But the proposed limitations will probably have little effect on Harvard-owned property and the University's development plans, Dowds said. Because Harvard Square is an "overlay district," it is not subject to the same variance requirements as other districts in Cambridge.

Instead of applying to the Zoning Board, the University must meet certain requirements, such as whether revenues from the proposed commercial development will help to save a historic building, he added.

But the petition could have some effect on several of the nine all-male final clubs, commercial properties which are in residentially zoned areas of Mt. Auburn St. Two final clubs--the Spee and the Phoenix--have received variances from city agencies in the past that permit them to house businesses in their basements.

In addition, if final clubs in residentially zoned areas were to sell their property, that land would then be restricted to residential use.

Harvard officials could not be reached for comment yesterday.

Geer said the petition was sparked by a situation a couple of years ago in which a residential area along the northern part of Mass Ave. near Porter Square was re-zoned as a commerical district by the Zoning Board.

"The Planning Board of Cambridge is currently suing the Zoning Board of Cambridge over the situation," said Dowds. "Basically the city had to hire two lawyers, and it's now spending a lot of time and money suing itself. The amendment to the ordinance would prevent that from happening again."

Residents also hope the petition will help the city develop a comprehensive and concrete development policy, said Jonathan S. Myers, a candidate for City Council who signed the petition.

"The city has no real policy as far as development goes," he said. "I and many other residents feel that development has gone too far. They feel that the city needs more housing instead of rampant commercial development."

The petition was first submitted to the city's Planning Board, which will hold a hearing on the petition, Geer said. No date for the hearing has yet been announced, he added. The board will then make a report which is to be in the hands of council members before a vote.

"There is, however, an unfortunate habit of providing it the afternoon of the vote," Geer said. "We're hoping to avoid that situation."

The proposed amendment will require a two-thirds vote of the council to pass, Geer said. However, should 20 percent of the property owners in the area object to the proposal, the required percentage of votes jumps to three-fourths.

"Since this is a citywide zoning proposal, it is quite a bit more unlikely that a contingent of 20 percent of the citizens will object," Geer said.

"I think it's got a chance," he said. "It will depend to some extent on the courage of the City Council, but I think it's got an excellent chance."