Jaguar/Land Rover: AM could share much with Jaguar sports cars, Jag doing the lower price mass produced cars and Aston the premium end of the market. Cost savings would be achieved. Also, an upmarket SUV based on the RR Sport would go down well I'd wager.
Toyota: They already supply tiny IQ cars, turned into plush offerings to reduce the company's carbon footprint. They could do the same as JLR, but working with Lexus.
Mercedes Benz: MB had a tie up with McLaren making top end cars for them, but this time top MB sports cars upgraded for the rarefied air AM operate in.
I don't think other brands would be suitable, because it needs to be a company that can provide top sports cars which both could use, albeit in slightly differing segments. Aston Martin deserve a quality car maker as an owner.