Catalyst, which owns 17.5% of Hudson's Bay, has bid C$11 per share, topping Baker's C$10.30 per share offer in October and valuing the company at C$2.03 billion ($1.53 billion).
Shares of the Saks Fifth Avenue owner rose as much as 14.3% to C$10.09.
Hudson's Bay on Wednesday confirmed that it had received the unsolicited proposal from Catalyst and that its special committee would review the offer.
Separately, the Baker-led consortium, which owns 57% of Hudson's Bay, said Catalyst's offer was "non-executable" and not supported by fully committed financing.
The group had previously said it would block the company's sale to another party.
Catalyst said on Wednesday it had filed a complaint with the Ontario Securities Commission over potential securities law violations in the consortium's C$1.9 billion deal.
The PE firm said it was prepared to consider raising the offer based on its due diligence and is open to allow other shareholders to be co-equity sponsors to its offer.
Activist shareholder John Litt, who has been opposing the Baker-led group's offer, said his hedge fund Land's & Buildings was interested in financially participating in the deal with Catalyst, should it move forward.
Reuters reported earlier this month that Catalyst was seeking financing for a rival bid for Hudson's Bay.
The buyout firm's all-cash offer represents a premium of 24.5% to Hudson's Bay's closing price on Tuesday.
(Reporting by Uday Sampath in Bengaluru; Editing by Maju Samuel and Anil D'Silva)
