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New home sales have struggled as builders face competition from foreclosures and short sales. While sales of previously occupied homes have risen more than 13 percent since July, sales of new homes fell in February for the second straight month and remain well below levels that economists consider healthy.

Lennar is offering its so-called “Next Gen” designs in states such as California, Texas and Florida. Sales of these multigenerational homes account for a small percentage of the company’s sales, but are growing quickly, said Jeff Roos, Lennar’s Western regional president.

Multigenerational homes are expected to account for roughly 30 percent to 40 percent of new homes in communities where the floor plans are offered, Mr. Roos said.

The Aliso Viejo-based New Home Co. is rolling out a range of options for multigenerational living in the affluent Orange County suburb of Irvine, where the Asian population has nearly doubled in the past decade.

The company’s floor plans include a self-contained suite attached to a main house or separate homes that share a common yard and pool. The company has reached out to Asian buyers by offering touches such as specially designed wok kitchens and dedicated music rooms, but the homes also are drawing buyers from other ethnic backgrounds, said Joan Marcus-Colvin, the company’s vice president of sales, marketing and design.

“Although extremely popular within the Asian culture, [multigenerational living] is also something a lot of other people are having to deal with,” she said.

Jim Park, vice chairman of the Asian Real Estate Association of America, said creating multigenerational designs is a smart move, especially in light of Asian-Americans’ preference for new construction and the community’s rising purchasing power.

“In my experience, people do move toward home products that are going to meet their needs better,” said Mr. Park, who owns a real estate firm in San Diego.

Builders said the tendency to live together longer comes down to a matter of economics as families of varied ethnic backgrounds cope with the wake of the recession and the needs of aging parents, whose retirement savings may have been depleted in the downturn.

“We see so many families that are living like this,” said Jeremy Parness, Lennar’s division president in Las Vegas. “There’s so many different reasons, all driven mostly by economics.”