Facebook’s record initial public offering is already oversubscribed, a source familiar with the share listing said, days after the world’s largest social network embarked on a cross-country roadshow to drum up investor enthusiasm.

Despite concerns about slowing growth, a lofty valuation and signs the company is having trouble ramping up revenue from mobile advertising, institutional investors have so far indicated demand for more shares than Facebook has available, the source told Reuters.

Analysts say the company, which is seeking to raise about $10.6 billion by selling more than 337 million shares at $28 to $35 apiece, may raise that price range if demand turns out to be healthy enough.

One large institutional investor had put in a major order for shares on Wednesday and was calling around syndicate desks trying to acquire more, a second source familiar with the IPO’s progress told Reuters, declining to be identified because the details are not public.

The company that began as Mark Zuckerberg’s Harvard dorm room project is expected to begin trading on May 18 after an IPO that dwarfs the coming-out parties of other tech powerhouses.