With demand for the Alibaba Group’s stock market debut proving even stronger than expected, the Chinese Internet juggernaut has done the only logical thing: set its fundraising sights even higher.

The company raised the price range for its initial public offering to $66 to $68 for each American depositary share, up from $60 to $66, according to a regulatory filing on Monday, pushing up its potential haul from the stock sale to as much as $21.8 billion.

That would value the e-commerce giant at $165.5 billion at the midpoint of the new range.

The new range was disclosed in an amended prospectus filed with the Securities and Exchange Commission Monday.

But while the order book is significantly oversubscribed — enough that Alibaba’s army of underwriters plans to begin closing order books this afternoon — the company and its advisers were conscious of not significantly raising the price range just because they could, according to people briefed on the IPO plans.

Potential investors have been eagerly awaiting the debut of the Chinese online market operator for months, with more than 800 people showing up at a lunch presentation in New York last week just to hear directly from the company’s executive chairman and co-founder, Jack Ma. Purchase orders have been coming in huge portions as investors place enormous orders in hopes of receiving even a fraction of the shares requested.

One hedge fund with about $3 billion in assets under management even put in an order for $3 billion worth of American depositary shares, one of these people said.

Alibaba and its underwriters have resisted bumping up the top of the price range to $70, as one news report suggested earlier Monday. Doing so may cost the Chinese Internet giant the bragging rights of having pulled off the biggest IPO of all time — a title that will stay with the Agricultural Bank of China, which raised $22.1 billion — but is meant to show that the company is looking out at the long term.

Nor has the company or the relatively few shareholders who are selling some of their holdings increased the number of shares available for the IPO.

One of the people with knowledge of the company’s plans said that if the IPO “left a little money on the table,” or did not raise as much as it could have, that would suit Alibaba’s management fine.