The investor group shopping for Macy’s is willing to pay a chunk more to secure the purchase of the department-store chain.

Macy’s stock surged Monday as Arkhouse Management and Brigade Capital raised their bid by nearly $1 billion. They increased their offer to $24 a share, or $6.6 billion, from $21 a share, or $5.8 billion. In response to Macy’s previous concerns over how Arkhouse and Brigade would be able to finance the acquisition, the firms said they had secured funds from Fortress Investment Group and One Investment Management.

It’s the next phase of an intensifying proxy battle over the company’s future after their previous offer was rejected in January. At the time, Macy’s board said Arkhouse failed to provide compelling value. Macy’s confirmed Sunday evening it had received and was reviewing the “revised, unsolicited, non-binding proposal.”

“The Macy’s, Inc. Board has a proven track record of evaluating a broad range of options to create shareholder value, is open-minded about the best path to achieve this objective and is committed to continuing to take actions that it believes are in the best interests of the Company and all Macy’s, Inc. shareholders,” the company said.

Shareholders appeared to be enthused by the revised offer, with the shares jumping 16% to $20.96 on Monday. Not only does the offer represent a 33% premium to the stock’s closing price on Friday, but it also increases pressure on Macy’s management to take the deal seriously, experts say.

“Although it was easy for M to dismiss the previous $21 offer given lack of detail provided by Arkhouse (originally), since this one comes with more info about Arkhouse’s equity partners (Fortress and One IM) and comments about financing the debt components of the transaction, we believe the [Macy’s] board is likely to more seriously consider the offer,” wrote Citi analyst Paul Lejuez in a note Monday.

That said, the stock was still trading below the offer price, in recognition of the fact it’s far from a done deal. For one, real estate angle transactions often don’t materialize, Lejuez noted. Investors may also decide that Macy’s is worth more and rebuff the offer, especially if they think that the company‘s latest turnaround plan—announced last week —has room to run.

The company plans to close about 150 unproductive stores in the long term—about a quarter of its footprint. It will reinvest in remodeling the 350 remaining Macy’s stores and in opening more small stores.

“It’s the classic dilemma of a bird in the hand is worth two in the bush,” said Neil Saunders, managing director and retail analyst at GlobalData. “You’ve got an offer there in front of you that’s quite a premium to the current share price. Do you take that? Or do you have faith in Macy’s management and this new turnaround plan that they’ve put in place to deliver value over a longer term?”

It’s a tough decision. On the one hand, new CEO Tony Spring has the chops and merchandising experience to pull off what Saunders calls a “very sensible” plan. On the other, Macy’s doesn’t have a great record of executing on its turnaround plans, he added.