There's a common mistake many entrepreneurs make once they've had their initial taste of success. Long before they've exhausted the growth possibilities of their first company, they decide to start another one in a totally unrelated business they know nothing about, and they end up spending time and money on it that should be put into building their original business instead. The risk is that they'll end up failing at both.

Let me tell you about Craig Howe, a young musician I know who started the Williamsburg School of Music in New York City's borough of Brooklyn about four years ago. He put together a faculty of professional musicians who give instrument and voice lessons to children and adults.

The school has had a promising start. Craig told me he has about 400 regular clients, fairly evenly split between adults and children. A single half-hour session costs $60, but almost everyone buys a package of lessons--five at $45 per session or 15 at $40 per session. The teachers, who work part time and have outside musical careers, earn about $30 an hour.

Growth is driven mainly by word of mouth, although many people learn about the school when they pass its storefront location on Bedford Avenue, one of the busiest streets in Brooklyn. It also has Groupon and LivingSocial deals that bring in prospects, about 70 percent of whom later buy packages of lessons. In addition, Craig has organized workshops in local elementary schools and met with parent groups to encourage more sign-ups.

Once clients sign up, they stick around--many have been students at the school since it opened, and children often stay in music school until they go to college. Adults, too, tend to remain enrolled for years, although some quit, for a variety of reasons.

"So what's the problem?" I asked.

Craig said he was bothered by the amount of time that his premises weren't being used. He pays a rent of several thousand dollars per month--retail space in the neighborhood is among the priciest in the country. Because the children come after school and the adults after work, music lessons happen only from 2 to 10 p.m. "Knowing how much I pay in rent," he said, "it just kills me that nobody uses the place in the morning."

He had an idea to open up a preschool nursery in the space. He knew I'd helped a couple of women with a children's play space in Brooklyn. He wanted to know if I would help him.

"How much do you know about starting and running a nursery?" I asked.

"Nothing," he said.

"Well, I'll be glad to tell you what I know," I said, "but it's the last thing I'd encourage you to do. I mean, here you have a business where you know what you're doing. It's your passion, and it's growing, and you really haven't had to go out looking for customers. They've come to you. Now you're thinking about starting a new business you know nothing about? A business, by the way, in which it's very hard to make money. And with a nursery, you have to get all new customers every two years or so. There's also a ton of paperwork and licenses you'll need. Then, even if it's viable, you won't be creating long-term value." I impressed on him that value in a business depends on things like recurring income from customers who come back year after year--in other words, exactly what he has at the music school, and what nurseries almost never have.

He obviously heard me. He left vowing to forget about the nursery and to focus instead on having the best music school in the city. I promised to help him. And who knows? Maybe we'll figure out what to do with the unused space along the way.