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Southeastern Asset Management intends to push harder against the buyout of Dell Inc. (NASDAQ: DELL) by founder Michael Dell and his partners. Southeastern, which owns a stake of about 8.44% in Dell, said in a Securities and Exchange Commission filing this morning that it has hired proxy solicitation firm D.F. King & Co. A logical conclusion is that King & Co. is being brought on board to launch a campaign against the $24 billion ($13.65 a share) takeover.

As we noted last week, for many Dell shareholders this takeover is really a “takeunder.” Shareholders who have owned the stock for about a year or more are mostly looking at an offer they can easily refuse. It is those investors that Southeastern will target.

Dell has a 45-day “go-shop” period during which the company and its advisers at Evercore may seek a better offer. There is a $180 million breakup fee for a successful competing bid, while any unsuccessful bid will boost the termination fee to $450 million.

Southeastern is pushing for a per share price of $24, well above the current offer. Dell stock has not traded above $24 since the summer of 2008.

Dell’s shares are trading today at $13.75, in a 52-week range of $8.69 to $18.36.