Begin with one formerly married couple and an amicable divorce (don’t snort, it happens). Add children, maybe two or three. Give each former spouse a new partner. Perhaps the new partners have children, too. Add them. Oh, and the new partners’ exes. Factor in an equitable (say, nearly 50-50) physical custody arrangement for all the parties.

What do you have? For many couples, it’s a complex data set in search of an equally complex algorithm to tame it. Do they move in together, mixing developing, separating teenagers like snarling cats in a bag? Or are they risk-averse, maintaining separate households and seeing one another on the odd weekend?

Or perhaps they are fortunate enough to establish some sort of contiguous living arrangement, like the members of the Curtis-Hetfield-Petrini household, who have as irresistible a scenario as anyone could devise.

On a recent bright Sunday, they were all at home together in their two-family brick town house in Brooklyn: Sarah Curtis, a 42-year-old preschool teacher; her daughter, Ella Hetfield, 10; John Petrini, 50, a molecular biologist; his daughter, Ramona, 13; and his son, Joe, 9.

They had all had breakfast in Curtis’ sleek, bamboo kitchen. Curtis made waffles; Petrini made bacon upstairs in his apartment and brought it down with him. The night before, they had had dinner at the Curtis-Hetfield dining table and then moved upstairs to watch “The Birdcage” in Petrini’s living room (his television is closer to the fireplace). Then they all retired to their own bedrooms, including Curtis and Petrini. (Hers opens to the garden; his is on the third floor. A pause to savor the luxury that each member of this family enjoys.)

“I do have to share a bathroom with my children, but I don’t have to share a closet with anyone,” Petrini said. “That’s very big.”

Theirs is a family model at the midpoint between Woody and Mia and Carol and Mike (as in Brady). It is a post-divorce living arrangement — you might call it the unblended or partially blended family — that some couples are pursuing to promote the well-being (and sanity) of both children and adults.

“We were both really concerned with maintaining a level of consistency with our children,” Curtis said. “And, quite frankly, I had been on my own for a number of years and I liked it. I was reluctant to give up that independence. We are committed to each other; we own a house together. I love our situation and the way it is divided up, but it’s not a marriage, it’s something different.”

Her mother was wary at first, Curtis said, but she has come around. During the renovation of the house, one of the roofers applauded a family bolstered by separate households. “He was an older guy, someone you’d expect to be very traditional,” Curtis said. “But he kept saying, ‘That’s the best idea ever!”’

The old, Brady Bunch stepfamily model — the “blended family” — has long been out of favor. Indeed, the term is almost universally loathed by family therapists for the unrealistic expectations it promotes of previously unrelated children blending harmoniously with one another and a new adult, and the disjunction between that rosy vision and the more prickly reality that is stepfamily life.

Into the breach pour all manner of scenarios: stepfamilies whose children move in and out of the home following various custody decisions; the nesters, whose children remain in the family home, while the parents move in and out on a schedule; the partial-blenders, like Curtis and Petrini; and the Living Apart Togethers, or LATs, to use the term for couples who maintain entirely separate residences.

As Susan Stewart, a sociologist at Iowa State University who studies how families form and change over time, observed: “The complexity of families is the real story. Family life is not what it was. The divorce rate” — roughly half of all first marriages still end in divorce — “has been high and stable since the 1980s. The majority of these people go on to marry or cohabit. Then there’s the change in custody patterns, with more and more fathers desiring more time with their children, if not full or shared custody. The traditional family — the married-couple-biological-children family — is in the minority.”

Today, there’s not one container for this new, many-tentacled thing called “a family.”

“Children are a disincentive to marry or cohabit,” Stewart said. “It’s why fewer women marry after divorce than men.”

But what’s really driving the practice of committed couples with children living in separate abodes, Stewart continued, “is that middle- and upper-income women have their own money and independence. They are working, and can live on their own.”

Just as Stewart, 42, does, maintaining her own house in Ames, Iowa, a few blocks away but on the same street as her ex-husband, with whom she shares custody of their 7-year-old daughter. Their daughter spends alternating weeks with each parent, “but it’s more fluid than that because we are both professors, we both have conferences for work,” Stewart said, and she “has to be picked up from this or that, so we talk and/or see each other every day because we are co-parenting.”

Stewart’s partner of three years, Christopher Missel, 37, an architect, lives 40 minutes away, in his own house in Des Moines. Missel has never been married, and is used to being on his own, but the real reason they don’t move in together, Stewart said, is her own need for autonomy after 13 years of marriage and a painful second marriage that lasted a month.

“I had bought a house with this person,” she said of her second husband, and the plan was to blend his family and hers. “My daughter was very attached. We divorced quickly, but the house didn’t sell for a year. I was still digging out from a lot of drama and financial complications when I met Chris.”

She continued: “If he and I were to break up, my daughter would be sad, but she wouldn’t be devastated, because I am able to keep both relationships relatively separate. It’s about ensuring that she doesn’t have another loss. Research shows that the well-being of a child is less about having an intact family, it’s about the number of transitions” — meaning, she said, a move or a new relationship that comes into the house.

“We know that kids with two married parents do better,” she said. “A lot of that can be explained by other factors like income or residential stability. For example, there is very little difference in the well-being of children from single-mother households and a household with a mother and a stepfather. But it’s one more layer of complexity.”

And couples who remarry have a 60 percent chance of divorcing; some demographers put that figure closer to 70 percent when one or both of the spouses have children from a prior relationship.

“Not cohabiting is a way of having a relationship when there’s a lot of obstacles,” Stewart said. “Not all women can do this, of course. It makes more economic sense to share resources. If I didn’t have enough money to live on my own, Chris wouldn’t be the best partner for me.”

Yet the economy is one factor freezing some new couples in place and apart.

Jenni Lorsung, 44, a writer in Burnsville, Minn., has three children from a 20-year marriage that ended a year and a half ago. Her ex-husband was her guarantor on the mortgage for her new house, she said, which she delights in running herself. She married right out of college, and had never lived alone.

Still, she would consider moving in with her boyfriend, John McNamara, 46, an architect, except that he lives across the street from her ex. “That would be awkward,” she said.

And McNamara would move in with her if he were able to sell his own house. “But the market stinks,” she said.

Another wrinkle is McNamara’s custody arrangement with his pre-teen son, whom he sees a day or so every other week, time he cherishes.

“On the practical side,” Lorsung said, “we’re dealing with three E’s: the economy and our two exes. On the emotional side, I wanted to make sure my kids were transitioning OK with their two new households. My sons would love for John to move in, or for us to move there. We joke it’s because he has an Xbox and I don’t. My daughter still struggles with needing time with me. I try to be responsive to that.” Families, she concluded, “don’t have to be two married people with kids — it can be this. That’s what we keep trying to say. This is a redefinition for us.”

Family therapists like to think of the state of maintaining separate residences as a temporary one, a transition toward moving in together, except in extreme situations.

Patricia Papernow, a clinical instructor in the Department of Psychiatry at the Harvard Medical School and a therapist who specializes in stepfamilies, recalled a couple who had moved in together — with his two girls and her three boys — with disastrous results.

“One of the daughters had major sensory processing issues, and she ended up in the hospital with a suicide attempt,” Papernow said. “It was all too much for this kid; the family cultures were just too different.”

She described a mashup of two divergent family styles: hers, loud, sporty and chaotic, with lots of sharing of stuff; his, quiet and neat, with distinct boundaries.

“It was easy for the grown-ups to say the girl was being manipulative,” she said. “But let’s define manipulative: ‘I’m trying to get something that I need and I’m going about it in this indirect way because nobody’s listening.’ The girl needed her father’s attention. Also, the adults were at each other’s throats. Perhaps if the adults had been able to stay calm and collected, things would have worked out differently. Or maybe not.”

The father and his two daughters moved out for a few years, but the couple stayed married. “It was very painful for the adults,” Papernow said. “They lost their daily contact with each other, but they also lost that incredible tension.”

It was an imperfect solution, she concluded, but then added: “It was imperfect if the idea was that we are all going to live together. But these are solutions to hard problems and we have to think outside the box. If you have to live in two boxes instead of one, that’s a much better solution than shoving everyone together in one box.”

Julie Friedman, a broker with Bellmarc Realty in Manhattan, recalled a scene at an open house she held last summer, in a three-bedroom apartment on the Upper East Side. A woman walked in and then burst into tears. As Friedman soon learned, the woman was divorced and had two children. She had recently sold her large Upper West Side apartment and moved in with her fiance, who had shared custody of his three children.

“She described the scenario as warfare,” Friedman said. “All the children were teenagers, and his were very territorial, landmines at every turn, and that soured the relationship between her and her fiance. After six months, he asked her to move out. Maybe not blending has merit.”

On the other hand, cautioned Friedman, who has a Ph.D. in social work: “Looking at this from family systems therapy, which emphasizes working through family dynamics to a resolution, a couple can’t completely unify when the dividing line is literally at the front door. While it’s beautiful to put your children’s emotional and physical needs paramount, by denying a bonded relationship with a new partner or spouse, you are sending a clear message to the children that they don’t have to adjust to new, possibly difficult scenarios and that the parent will defer to the child through sacrifice and martyrdom.”

Of course, in New York City, everything is possible, Petrini moved to his three-bedroom apartment in Brooklyn four and a half years ago from Manhattan, so his children could be closer to his ex-wife, who had also moved and with whom he shares custody. In 2007, when the house came on the market, he and Curtis, who were already involved, bought it together, at which point they renovated, creating two very individual containers for each household.

There is a clear aesthetic dividing line between the two — a psychological division — in addition to the staircase. The front hall is open to Curtis’ parlor-level living room, and to the stairs up to Petrini’s apartment. Curtis’ daughter, Ella, spends every other weekend and every weeknight here but Tuesday, when she is with her father in Manhattan. Petrini’s children, Ramona and Joe, are here every weekend, and Wednesday nights.

The contiguous apartment scenario eliminates some basic stepparenting snags — Ella is expected to make her bed, and if Ramona and Joe were living in Curtis’ house, they would be, too, and that’s a turf battle everyone is happy to avoid. But it preserves many of the benefits.

“I was worried about Ella being an only child,” Curtis said. “Years ago I had considered adopting, but then I worried how a child with no father would feel as the sibling of a child with a very involved father.”

But the Petrini-Hetfield clan consider themselves siblings, all three said. “Joe and I fight like brother and sister,” Ella said proudly.

Sitting in the sun-filled parlor, with Ella and Joe perched on either side of her, Ramona added:

“Sometimes I feel like this family — it’s more picturesque than my mom’s family, which is a single mom with two kids. Sometimes I feel bad that it looks this way, though my mom understands that she is more unorthodox. As comfortable and nice as it is here, it’s not better, it’s just different.”

Like any family, this one has evolved its own rituals. On Christmas, that means two trees, one for each household — hers with white lights; his with colored — and a night of decorating both.

“It started out as a competition,” Petrini said. “And now it’s this great tradition.”

© 2010 The New York Times Company