Over in the Marvel forum, a really interesting idea was posted:
First things first: this would be tricky, because it pretty much requires a constant low-grade crossover to be worthwhile.
My first thought here was Poison Ivy. She has been shown as friend (or ally) with both Barbara Gordon and Swamp Thing, and arguably should go together well with Wonder Woman and Aquaman. At the same time she is clearly an effective antagonist against Bruce Wayne even more than Batman and most other DC heroes. But she is in limbo right now.
Giganta is another possible example, as an enemy of Wonder Woman but in an on-again off-again relationship with The Atom.
As formerly bad characters having a tenuous relation to the law and morality, I can see Harley Quinn and Plastic Man having good relations with a lot of villains.
I can see Bruce Wayne and Lex Luthor being extremely impressed with each other, having no problems understanding each other, but at the same time being so competitive that there is no room for any friendship in the normal sense.