Technically, Dell (NASDAQ:DELL) is still on the market, at least until March 22.

Even though the $24.4 billion buyout offer orchestrated by private equity firm Silver Lake and the chief executive and company founder, Michael Dell, was accepted — as part of the original deal — the company agreed “to explore in good faith” any other proposal that was submitted to its board of directors during the 45-day go-shop period. These terms were meant to give Dell the opportunity to look for offers from other companies to guarantee it has agreed to the best possible proposal.

At the time the $13.65-per-share deal was made, Dell was not expected to find another offer. Hewlett-Packard (NYSE:HPQ) and Lenovo (LNVGY.PK) — the two largest makers of personal computers, ahead of Dell — have inspected Dell’s books after signing non-disclosure agreements, as sources familiar with the matter told Bloomberg. However, no offer has been forthcoming.

Blackstone Group (NYSE:BX) also took a look at Dell’s books and, as the publication reported Tuesday, is weighing a bid of its own. There is already a link between the two companies; Dave Johnson, the former head of Dell’s Mergers and Acquisition unit, joined Blackstone last year as a partner in the technology group.

Mr. Dell began the company in his college dormitory room in 1984, and it eventually grew into one the world’s largest computer manufacturers. But competition from other personal computer companies and the transition away from desktop computing has eroded his business. As a private company without shareholders, Mr.Dell will have much more control to engineer a turnaround. He has angled for such a deal since last August, when he first approached the board regarding a leveraged buyout, and it is his most drastic attempt to reform the business.

Given the problems hurting the PC industry as a whole, and Dell in particular, securing financing was initially difficult; before the deal to go private was finalized, many analysts assumed that the company’s “lack of an exit strategy” would discourage potential investors. Yet, even with this sizable hurdle, several of the company’s largest shareholders — including activist investor Carl Icahn and Southeastern Asset Management — have voiced their opposition to the buyout price. For them, the interest of Blackstone is good news, as an additional bid will drive up the final offer, no matter which entity eventually takes Dell private.

“If Blackstone were to make an offer out there, I don’t think that’s the end game,” Standard and Poor’s analyst Angelo Zino told Bloomberg. “Then Michael Dell has to revisit his $13.65 offer. That could lead to a bid as high as $15 a share.”

At $15-per-share, Dell would being going private for an amount approximately 5.4 times its earnings before interest, taxes, depreciation and amortization — the lowest multiple for a technology buyout larger than $1 billion, according to data compiled by Bloomberg.

Still, this price is much closer to what the company’s shareholders think Dell should be valued. While the value of the company is directly related to the viability of its business, and Dell’s business is clearly suffering as PC shipments continue to fall, Southeastern Asset Management has listed $20-per-share as a more reasonable price. Dell would do well to consider the grumblings of its shareholders as the bid from Silver Lake requires approval from a majority of shareholders, excluding Michael Dell and his 15.6 percent stake.

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