Kenney Farm Concord expanded to produce multiple varieties of vegetables for the Faneuil Hall Market in Boston. In the late 1930's, with assistance from Billy's brother Tom, Kenney Farm Concord started direct sales to the A&P Supermarket chain. Eventually Kenney Farm Concord produced exclusively for the A&P chain. With the death of Billy Kenney in 1942, Phil and Lawrence assumed ownership of the farm. Under the management of Phil and Lawrence, Kenney Farm Concord grew to approximately 150 acres with the purchase and leasing of local farmland. In the early 1960's Phil retired from farming. With his son Billy, Lawrence continued operating his portion of the farm until his death in 1993 at the age of 81.

Kenney Farm Concord continued producing vegetables for wholesale market to The New England Produce Market, Shaws Supermarket, Stop and Shop Supermarket and local farm stands. In 2010, after many years of wholesale production only, Kenney Farm is adding a CSA to the operation. This market strategy is based on the growing interest of the consumer receiving the locally-grown vegetables directly from the grower.