MELISSA FLOTH and her three-year-old son spent months sleeping on friends' floors until she found affordable housing. Although she gets only $560 a month from welfare, she now shares a comfortable house with three other single mothers, thanks to the unusual Bay Area group Innovative Housing."If it wasn't for this program, I don't know where I'd be now," says Ms. Floth, holding her squirming son Nicholas. The nonprofit, private corporation Innovative Housing leases just over 100 houses in five Bay Area counties and rents them to small groups of people. By sharing rent and some household expenses, homeless, low-income, and elderly people can afford decent housing. Sanford M. Dornbusch, director of Stanford University's Center for the Study of Families, Children, and Youth, considers Innovative Housing a national model. "They create a wonderful esprit de corps," he says, "and they save a lot of money." Ms. Floth participates in one of Innovative Housing's four programs. This two-year transitional program aims at getting homeless, single mothers off welfare and into permanent housing. She and Nicholas live in one room of a four-bedroom house in Mountain View, Calif. A one-bedroom apartment there normally rents for $600 to $700 a month. But Floth pays only $156 for rent and utilities. She says she saves $56 each month toward a future rent deposit. Much of the rest of her Aid to Families with Dependent Ch ildren check goes for food and to repay debts. Each roommate pays about 30 percent of her income for rent and utilities but must buy and cook her own meals. The house assigns everyone household chores. If anyone skips a week, "we get on 'em," says Floth. Innovative Housing helps find regular child care during the day. Floth says she will soon enroll at a local community college and is looking for part-time work. "I want to get off welfare," she says, "and get an apartment of my own." To the nodding agreement of two other women in her house, Floth notes a drawback to collective living with strangers: "We get on each other's nerves. But we also help calm each other down." Judith Steiner, Innovative Housing director for Santa Clara and San Mateo counties, says her organization provides dispute mediation for such problems. When needed, it also directs the women to substance-abuse counseling, job training, and education facilities. She says that Innovative Housing's programs can be duplicated elsewhere, but it seems relevant mainly in areas "where housing costs are such that people are already doubling up," such as New York City, cities in northern New Jersey, and Washington, D.C. Professor Dornbusch says Innovative Housing "serves as a good model, although you can't reproduce it exactly." He says he admires its method of working intensely with a small number of people over several years, which helps the homeless make the transition back into the job market. Innovative Housing's current shared living arrangements wouldn't work with certain kinds of homeless people such as chronic substance abusers or the mentally ill, Ms. Steiner concedes. "Shared housing requires a minimum level of social skills," she says. "People who are severely dysfunctional require somebody living in." For those homeless people, she adds, Innovative Housing is "looking at modifying motels so people have individual units, but there's common shared space."