Updated with Carmike response: Carmike’s largest shareholder, and most vigorous critic of its $1.1 billion (including debt) sale to AMC Entertainment, turned the screw a little tighter today.

Investment firm Mittleman Brothers told the company in a letter that it raised its stake to 8.4% from 7.1% — and warned that it’s “highly confident” shareholders will reject the AMC deal if Carmike doesn’t scrap it. Managing Partner Chris Mittleman adds that his company won’t solicit proxies.

The investor says that Carmike sold itself too cheaply by accepting AMC’s offer of $30 a share. Mittleman believes the No. 4 chain is worth at least $35 a share in stock or $40 in cash.

AMC offered $37 in March 2015 but withdrew after Reuters reported that Carmike had hired a bank to look for a buyer — news that boosted its stock price. Carmike says that AMC was the only bidder when it finally reached an agreement last month.

But Mittleman says that Carmike “bizarrely” didn’t check out private-equity firms that might have made an offer.

“Carmike’s board compounded their error by agreeing, in negotiation with AMC as a single potential purchaser, to a no-shop agreement, thus excluding this vast potential buyer group” that might step up, the letter says.

The investor adds that the board should have created a special committee to oversee the process. CEO David Passman had conflicting interests, it says: He can collect “substantial golden parachute compensation” in a sale — worth about $8.4 million — and had “no prior experience in negotiating a public company merger.”

“While we certainly do not begrudge David Passman’s well-deserved golden parachute after seven outstanding years of leadership yielding excellent operating results, it cannot be fully condoned in conjunction with such a poor exit package for non-management shareholders,” Mittleman says.

What’s more, board Chairman Roland Smith “was likely distracted” during the negotiations. He’s CEO of Office Depot, “which has been in a high-profile battle with the Federal Trade Commission in seeking approval for a merger with Staples.” In December, the FTC sued to block Staples’ $6.3 billion deal to buy Office Depot.

If AMC refused to offer more than $30, then “Carmike should have simply walked away, to continue growing the business as you have done so well over the past seven years.”

Carmike says that while it “appreciate[s] Mittleman’s views as a shareholder, we do not share their perspective.”

The deal with AMC “is the result of a thoughtful review of Carmike’s strategic alternatives” with advice from J.P. Morgan and King & Spalding and the board’s unanimous support.

AMC’s $30 offer “represented an approximate 19.5% premium to Carmike’s stock price,” making it similar to the premium in the $37 proposal that AMC made in March 2015, but then withdrew.  It’s a higher multiple of the company’s earnings “than any comparable, large-scale theatre transaction multiple over the last 10 years.”

The exhibition chain adds that “After contacting multiple potential buyers, Carmike did not receive any offers that provided greater value than AMC’s $30 per share offer.”

Wall Street still believes that the deal with AMC will go through “with limited divestitures,” Stifel Research’s Benjamin Mogil says.

Wedbush Securities’ Michael Pachter said last week that Carmike’s selling for “a reasonable valuation” and that investors should not “expect a higher outside bid prior to the closing of the acquisition at the end of 2016.” He forecasts that AMC will have to divest as much as 30% of Carmike’s screens to pass muster with antitrust officials.

Carmike shares closed Friday at $30.06, up 0.2%.