The "Grey's Anatomy" star is trying to purchase the coffee chain, but AgriNurture Inc., paired up with Starbucks, is willing to bid more money.
AgriNurture Inc. says it's still willing to proceed with its combined bid with Starbucks of about $10.6 million. The bid from Dempsey's company, Global Baristas LLC, was for $9.2 million.
The proposed sale goes before a bankruptcy judge in Seattle on Friday.
Starbucks has said it wants to convert some of Tully's cafes to its own brand, with AgriNurture running the rest under the Tully's name.
AgriNurture, based in the Phillipines, also does business in the U.S. as Earthright Holdings Inc.
Another bidder has also filed an objection to the sale, saying the rules changed in the middle of the auction.
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