Several major shareholders of McGrow-Hill Inc., including family member Donald C. McGraw Jr., will meet this weekend to decide whether to sue or take other action against the publishing company's directors for voting to reject a $40-a-share takeover bid from American Express Co.

American Express Monday with-drew a hostile $34-a-share takeover bid and told McGraw-Hill directors it would up the ante to $40, but only if the directors either approved the offer or agreed not to fight it.

American Express hopes that the threat of possible shareholder suits would force McGraw-Hill's board to stop it legal attempts to block the credit card company from making the offer.

But the board Wednesday unanimously backed Chairman Harold W. McGraw Jr., rejected the offer and sent a letter to stockholders denouncing the new, higher-priced offer.

American Express Chairman James D. Robinson III said he was surprised by the swiftness with which the board rejected the new proposal but said he would keep the offer open until March.

The $40 offer is $16 a share higher than McGraw-Hill stock closed on Jan. 8, the day before the first bid was made public. The publishing company's stock climbed to $31 3/4 a share by last Friday and did not trade after that until today.

McGraw-Hill was the most active issue on the New York Stock Exchange today, closing down $2 1/2 a share at $29 1/4.

Some major stockholders, such as Donald McGraw and Maxwell M. Geffen, have said that stockholders in the giant publishing firm -- that owns Business Week magazine and Standard & Poor's financial rating service -- should have the opportunity to consider the American Express offer.

But American Express has said it will not make a formal offer as long as the board continues to fight, although it remains willing to do so if there is a change in heart by the board.

American Express officials say privately that they hope a spate of shareholder suits might convince the board of directors to change its posture.

Donald McGraw, who owns 622,000 of the company's 24.5 million out-standing shares, has said he would join a class action suit to force the board to permit the offer to be made.

Reached in Florida today, Donald McGraw said that major shareholders including himself and Geffen would meet this week to decide what course of action to take.

Geffen, in New York, said he feels "very strongly, as a matter of corporate democracy, that the board should allow stockholders" to consider the American Express offer.

Asked whether he favored filing a suit to force the board to permit the American Express offer to be made, Geffen said, "I am not a litigious character," but added that he would have to consider carefully whatever a "responsible group of individuals such as Donald McGraw" and others decide to do.

The major shareholders could also decide to wage a proxy fight to try to wrest control of McGraw-Hill from the current board, although such a fight probadly would be bloody. Donald McGraw was ousted as an officer of the company two years ago by his cousin Harold. He remained on the board until last April, when he did not stand for re-election.

Whether McGraw-Hill's directors would be willing to change their minds under a spate of suits from major shareholders is unclear. They knew that suits might be filed -- one in fact was filed more than a week ago when the offer was at $34 a share -- when they made the unanimous decision.

McGraw-Hill carries $10 million worth of liability insurance for its officers and directors. The difference between yesterday's closing price of $29 1/4 and the $40 offer is about $250 million for the 24.5 million outstanding shares of McGraw-Hill.

McGraw-Hill has opposed the merger for a fvariety of reasons, citing the need to protect the integrity of Business Week and Standard & Poor's. The company has also charged that American Express President Roger H. Morley violated his fiduciary reaponsibility to McGraw-Hill by serving as a McGraw-Hill director at the same time his company was considering a takeover.