(Sorry I haven't updated in forever, but my lack of ideas is troublesome. So, here are some headcanons and feel free to comment an idea or two for a story if you've got one.)
* Greed tends to be rather sexual when teasing and such but gets genuinely confused when he gets a positive response.
* Ling likes to give Greed bad advice about people especially if Greed happens to really like them. He gets some joy out of watching Greed get flustered when he's taken some of Ling's more ridiculous advice.
* Greed constantly feels the need to hold on to his S/O (significant other) physically. Part of his protective nature.
* Greed is always ready to throw down for his S/O. He's very prone to trying to fight people over minimally inconveniencing his S/O. Stop him.
* Ling and Greed like to switch control from time to time just to see how long it takes for people to notice.
* Greed thinks it's the most adorable thing when his S/O wears his coat especially if it's far to big on them.
* Greed can be the biggest dork when it comes to his S/O. Ling very much enjoys teasing him for it.
* While Lan Fan doesn't like Greed, she actually doesn't mind his S/O. She is slightly uncomfortable about the relationship given Ling and Greed share a body.
* After Greed dies, Ling makes a great effort to comfort Greed's S/O and makes sure they're taken care of in any way he can. He even offers to take them back to Xing. They both grieve for Greed together.
* Greed gets hell when Ling and his S/O team up to tease and embarrass him.
* I can definitely see Ling and Greed's S/O being best friends.