The world’s No. 2 brewer is holding out for a higher bid because it believes it’s worth more than No. 1’s latest offer of $104 billion. SABMiller’s board is citing its exposure to attractive emerging markets like Africa, where beer consumption still greatly trails the global average.

But analysts and shareholders don’t seem convinced SABMiller has much room to demand a higher price. Shares barely edged up on Wednesday after the brewer nixed AB InBev’s latest overture, and analysts see only a few more bucks added to any sweetened offer.

AB InBev (BUD) tried twice to make a deal happen behind closed doors and then went public with its third proposal of 42.15 pounds a share ($65) in cash, a premium of 44% over where the shares were trading before news of AB InBev’s intention to bid leaked out last month. The deal gets a bit complicated, because that price is for 59% of SABMiller shares, with a partial share alternative valued at 37.49 pounds a share for the other 41%, consisting mainly of equity in AB InBev plus some cash.

A deal would generate the only major beer producer to operate on all six populated continents, creating a truly global player with high profit margins and several key medium-term growth prospects. It would unite SABMiller’s portfolio of Miller, Coors, and Peroni with AB InBev’s Budweiser, Stella Artois, Beck’s, and Hoegaarden.

AB InBev CEO Carlos Brito, speaking during a conference call Wednesday, said his company could finally get key beers like Corona and Budweiser distributed in Africa and other key markets where those brands aren’t stocked.

Analysts say there is some room for AB InBev to boost its offer by a few more pounds, but they don’t see a lot of negotiating room for SABMiller’s board. The company is partly blocked in by the support AB InBev has won from U.S. tobacco giant Altria (MO), which controls a nearly 27% stake in SABMiller. In a separate statement on Wednesday, Altria said it would support a 42.15 pound-per-share offer or anything above that price. Another large SABMiller shareholder, privately held Bevco, hasn’t yet backed the deal.

“We’d still be supportive up to £46 but lower bid now likely accepted,” wrote Sterne Agee CRT analyst April Scee in a research note. Other analysts who spoke to Fortune said they could see room for the offer to go up to as high as 43.50 pounds a share, but they’d be surprised if it went above 45.

Bonnie Herzog, a U.S.-based analyst who covers Altria, also sees some room for a higher price that would be advantageous for the tobacco company’s shareholders. Herzog—who accurately predicted Reynolds American (RAI) would buy rival Lorillard—sees a 60% to 70% probability the AB InBev-SABMiller deal will close.

While SABMiller Chairman Jan du Plessis contended the offer “very substantially” undervalues his company, it is notable that SABMiller hasn’t raised any concerns about regulatory hurdles—language often cited when a takeover target doesn’t ultimately want to sell.

Observers and even AB InBev itself have conceded that divestitures would be needed in the U.S. and China markets. As Fortune previously reported, SABMiller’s stake in the MillerCoors joint venture would almost certainly need to be offloaded. For U.S. assets, Molson Coors (TAP) is best positioned to buy the stake in MillerCoors that it doesn’t already own. Few rival bids are expected to drive up the price for that stake.

Its biggest hurdle, AB InBev acknowledges, is the SABMiller board.

“In every transaction, people ask about the risk. The biggest risk is the way the board is behaving,” Brito said. “The fact that they have not engaged after repeated increases in our offer tells us that they are the biggest risk to this transaction.”

That’s why it was important for AB InBev to make the deal public to shareholders, Brito said, to give them a say in how things shake out.

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