Dell Inc. said it got proposals from Blackstone Group LP and Carl Icahn that may be superior to Michael Dell’s $24.4 billion buyout plan, putting more pressure on the founder to sweeten his bid for the computer maker.

Blackstone’s plan values Dell at more than $14.25 a share, while Icahn would pay $15 a share in cash for as much as 58.1 percent of the stock, Dell said today in a statement that included their offers. Under both plans, some shares may continue to be publicly traded. Michael Dell, who proposed $13.65 a share, is willing to work with third parties on the alternative plans, the company said.

The challenges to the original bid, which came as Dell struggles to catch up with a new wave of nimbler competitors in mobile computing and business services, mean Michael Dell could lose control of the firm he founded in his Texas dorm room in 1984. His plan, backed by partner Silver Lake Management LLC, was to retool Dell as a maker of data-center gear and software for corporations -- without the scrutiny of public investors.

“Blackstone and Icahn are financial buyers, not ego buyers, and their name isn’t on the door, so they won’t stay in a bidding war that requires them to overpay,” said Erik Gordon, a business and law professor at the Stephen M. Ross School of Business at the University of Michigan in Ann Arbor. “That’s Michael’s advantage, assuming his goal is to keep the company at any price.”

Dell rose 3 percent to $14.57 at 9:43 a.m. in New York, 6.9 percent above Michael Dell’s offer.

Blackstone is proposing a leveraged recapitalization transaction. Investors could choose to get either all cash or equity, subject to a cap, if they want to stay invested in Dell. The shares would continue to be publicly traded.

Blackstone, which has teamed up with Francisco Partners, a San Francisco-based technology-oriented buyout shop, and New York-based venture firm Insight Venture Partners, said it plans to fund the transaction with a combination of equity and debt financing, in addition to using Dell’s cash and equivalents. Blackstone said it held discussions with some of Dell’s largest shareholders and plans to invite them to join the transaction.

Icahn is offering shareholders the option to roll over their stakes or receive $15 a share in cash, with the amount of cash to be used limited to $15.65 billion, according to the statement. The offer assumes that Southeastern Asset Management Inc. and T. Rowe Price Group Inc., among the largest Dell investors after Michael Dell, would contribute their stakes and won’t receive a cash payment. If the cash portion is fully used, it would result in 1.04 billion shares, or 58.1 percent of current shares outstanding, being acquired. If fewer shareholders decide to sell, the cash not needed would be distributed as a special dividend.

T. Rowe Price declined to comment, Brian Lewbart, a spokesman, wrote in an e-mail. Lee Harper, a spokeswoman for Southeastern, didn’t respond to an e-mail seeking comment.

Dell’s special committee for the go-shop process, during which the buyout target can solicit competing offers after the initial agreement, hasn’t determined that either the Blackstone or the Icahn proposal in fact constitutes a superior proposal, according to today’s statement. While talks are ongoing, the committee continues to support the buyout proposal.

Under terms of the original Feb. 5 agreement with Silver Lake, the board will take time to determine whether the counteroffers are superior. If the board accepts a new offer, it is required to give Silver Lake and Michael Dell at least four business days’ notice to top it. Michael Dell, who owns 15.6 percent of the stock, and Silver Lake have just one chance to top it.

At least five analysts surveyed by Bloomberg earlier this month saw the buyout group increasing the bid to as much as $14.90 to $15 a share.

“Michael wants to play a role here,” said Jayson Noland, an analyst at Robert W. Baird in San Francisco, who has a neutral rating on the shares. “This is his company -- it’s been his life, his name’s on the door and he’d like to be part of the next stage,” he said. “The most likely scenario is Silver Lake and Michael Dell take this company private for something north of what they’re currently offering.”

At $15, Dell still would be going private at about 5.4 times earnings before interest, taxes, depreciation and amortization, the lowest multiple for a technology buyout larger than $1 billion, according to data compiled by Bloomberg.

For the 48-year-old chief executive officer, once part of a technology-industry pantheon that includes Microsoft Corp. co- founder Bill Gates and Oracle Corp. CEO Larry Ellison, prevailing in a surprise takeover fight could help in the effort to restore Dell’s reputation and performance. Once the world’s largest maker of PCs, Dell has floundered as those machines have been eclipsed by tablets and smartphones from companies such as Apple Inc. and Samsung Electronics Co.

“Dell is the most challenged company in my coverage universe, and two-thirds of their business ships with a hard- disk drive attached,” said Brian Marshall, an analyst at ISI Group in San Francisco, contrasting Dell’s PC-related business to mobile devices that user faster forms of memory. “Two-thirds of their revenue is commoditized. People are very cautious and leery,” said Marshall, who has a neutral rating on the shares.

Blackstone and Icahn submitted their proposals on March 22, the deadline of the go-shop period. Southeastern Asset Management and T. Rowe Price have said they would oppose the original buyout offer because it is too cheap.