What business makes no money, has yet to pass its third anniversary and just turned down an offer worth billions of dollars? Snapchat, a social media platform run by a pair of 20-somethings who until last month worked out of a beachfront bungalow in Venice, Calif.

Thanks to today’s rabid rat race for the hottest social media startups, Snapchat has joined the list of tech companies — like Tumblr and Instagram — with no money coming in but multiple sky-high takeover offers.

So far, Snapchat’s leaders have balked at the offers, according to three people with knowledge of the overtures, including a recent multibillion-dollar proposal from Facebook, the biggest social network of them all.

It’s not that they don’t want billions of dollars. In part, it’s because they think making a deal now would leave many billions more on the table.

The service, started in 2011 by Evan Spiegel and Bobby Murphy, two former Stanford fraternity brothers, lets users send photo and video messages that disappear after they are viewed. Snapchat quickly gained a reputation as an easy way to send sexually suggestive photos, but it also picked up steam among young users as a fun and easy way to trade photo messages.

The company has in recent months become one of the most sought-after businesses in the tech industry, getting attention from top Silicon Valley companies and venture capital firms, as well as international technology companies.

In the past, several startups found even greater success by passing up a billion dollars or more, including Facebook and Twitter. Even Twitter, with its red-hot debut on the public market, still has skeptics who question whether it can grow enough to justify its current market capitalization of more than $20 billion.

But Silicon Valley is littered with many more entrepreneurs whose big dreams went unfulfilled, people who were at the helm of the next big thing and lost momentum before they could cash out.

"I think this is classic bird-in-hand versus bird-in-bush," said Julie A. Ask, an analyst at Forrester Research. "Snapchat must believe the bird-in-bush is bigger."

Snapchat recently said that it now processed upward of 350 million messages a day. In February, the company was processing 60 million a day.

That rocketlike growth has emboldened Snapchat’s leaders to hold out for a better deal, and with a suitor of their choice, at least for now.

© 2013 The New York Times Company