Investor Jack Kent Cooke, who counts the Washington Redskins and the Chrysler Building among his many holdings, yesterday increased his offer for Multimedia Inc. to $1.08 billion.

And Cooke indicated he might go even higher to get the South Carolina-based company, which owns newspapers, broadcast stations and cable operations and produces the "Phil Donahue Show."

Multimedia, which balked at Cooke's earlier $1.05 billion offer and two slightly smaller recent offers from other suitors, said it would present Cooke's latest proposal to its founding stockholders, but cautioned, "There should be no assumption that a transaction with Mr. Cooke will occur." Multimedia's biggest stockholders, including its founding families and managers, are attempting a leveraged buyout of the company.

The founding families and management own more than half of Multimedia's stock. So far, they have shown no interest in selling the company, and in fact, Cooke said in a statement yesterday, they have taken a number of steps to prevent him from buying the company. Cooke said the founding families have agreed among themselves not to sell their stock to him and have offered a piece of the company following the leveraged buyout to Wall Street arbitrageurs and money managers in exchange for their support of the leveraged buyout plan rather than Cooke's offer.

"The intended effect of this is to block my attempts to offer shareholders a better price for their shares," Cooke wrote in a letter to Multimedia's board in which he proffered his new bid. "Unless the intended effects of these agreements with the stockholders and the arbitrageurs and institutional investors are rescinded or declared ineffective, unaffiliated shareholders will never have a fair opportunity to consider competing offers."

Cooke asked for the help of Multimedia's management in overcoming the "major hurdles"' thrown in his way by the major stockholders.

Cooke could not be reached for comment on his offer.

In his new bid, Cooke offers to pay $65 "or more" for each of Multimedia's 16.7 million shares, up from his earlier bid, made two weeks ago, of $63 a share. Multimedia stock closed yesterday at $57.50 bid in over-the-counter trading, up $1.12.

In addition to rejecting Cooke's earlier offer, Multimedia also has turned down offers of about $1 billion each from a group headed by former Treasury secretary William Simon and from Lorimar Productions, a film and television production firm.

Multimedia's own leveraged-buyout plan, which would offer shareholders a combination of cash and securities, has a total face value of about $67 a share, or roughly $1.11 billion. But Cooke said in his letter yesterday, "I am convinced that the transaction which I have summarized above represents a substantially higher monetary value to the shareholders of Multimedia than any transaction proposed by any other party which has been publicly disclosed."

Cooke said in the letter that he would keep Multimedia's management in place if he took over the company and that he would not break Multimedia up. "Rather, I fully intend to pursue additional opportunities for acquisitions to expand the current holdings of Multimedia," Cooke wrote.

Multimedia owns 43 newspapers, 5 television stations and 10 radio stations, and operates more than 100 cable systems. Last year, it had revenue of $304.4 million and income of $33.6 million.

Cooke has extensive real estate holdings and is chairman of cable television's Group W Cable.