Plans for the aging Parkington Shopping Center in Arlington keep growing. May Centers, owner and developer of the 30-year-old complex, this week announced the addition of a fourth level of shops, restaurants and movies and a third department store to firm plans for the redeveloped mall.

In addition, Forest City Rental Properties Corp., a large national developer of commercial real estate, has entered the project as a partner with May Centers.

Forest City, with $250 million in annual revenue, operates 14 million square feet of retail space in malls stretched actress the nation, in addition to residential development.

A face lift for the shopping center, situated a block from the Ballston subway stop, first was discussed in 1979. At that time, the renovation plans called for expansion of the present 27-store, one-level mall to two levels containing 30 shops. In addition to the smaller shops, Hecht Co. and J.C. Penney department stores are part of the center.

During the intervening years, the opening of the Metrorail station and I-66 nearby have encouraged developers and county officials to believe that the down-at-the-heels Ballston neighborhood can become a major shopping, office and residential hub.

A glut of office space and the recession have slowed the pace of development in the last three years, and Metro has been unable to attract bids for development of the land it owns around the subway station. Although the oversupply of office space has not dissipated, the recession has eased.

May Centers and Forest City plan to begin construction early next year at Parkington, which has been renamed Ballston Common. The new, $100 million mall is expected to be finished and open by the fall of 1985, said John D. Moore, vice president for development for May Centers.

An addition to the plans is for a below-ground level of restaurants, fast-food shops and movies. Three levels about it will be occupied by more than 100 stores "of a contemporary merchandise mix," according to John D. Moore, vice president for development for May Centers, which is part of May Department Stores Co., the owner of the Hecht Co. The Hecht store at Parkington will be refurbished and reduced "to a more manageable size."

The developers and J.C. Penney are "at an early stage of discussion" over whether Penney will remain in the mall, said a spokesman for the department store chain.

"We have had discusions with the developer of the shopping center regarding his plans and how we might fit into them," said the spokesman. He added that a decision could be months away.

A nine-story office building will rise atop the mall. The Oliver T. Carr development company this week withdrew from negotiations for construction of the office tower, saying "we weren't successful" in reaching an agreement with May.

Negotiations with another developer are under way, with announcement of a decision expected in "a month or two," said Ian Bacon of the Cleveland-based Forest City corporation.

A third department store, discussed in the past, now has been made a permanent part of plans for a later stage of development on the 13-acre site, Bacon said.

"We have no takers at all for the third store. It will probably be two or three years before anyone takes it," he said. In the meantime, the site, next to the Hecht store, will be landscaped, he added.

Office floors will be built atop the third department store, either at the same time that the store is constructed, or later, Bacon said.

Later stages of development also will include construction of a triangle-shaped office building at the intersection of Glebe Road and Wilson Boulevard, containing 330,000 square feet of offices and 25,000 square feet of retail stores.

Parking for the new mall will be constructed with the help of tax-free revenue bonds, which Arlington County will sell.

Officials of the county are delighted that start of construction on Ballston Common finally seems near. There are no major shopping malls in the county,

County economic development chief Tom Parker said Arlington expects tax revenue of $3 million annually for 10 years after the mall's opening. This is last year's estimate based on plans before the third department store was added to the development schedule, he said.

When all three office building are constructed and leased, they will house about 3,800 employes, Parker said.

A pedestrian bridge over Wilson Boulevard eventually will connect Ballston Common with the Metrorail station, said Moore. The developers and the county will share the cost, he added.

The bridge would cross from the center to a complex of residential, office and retail buildings that Metro hopes to build on its property around the subway station.

When Metro asked for bids on the Ballston development during the depths of the real estate slump last year, it had no response. The transit authority now has "entered preliminary discussions" about development with the owner of property adjoining Metro's, said Henry W. Cord of Metro's development branch.