I know it's technically cheating since I already used Black Swan in a pair with Shame, but that was years ago and as for potential pairing up with Suspiria, Swan has way more visual parallels with Refn's latest, so I went with that one.
Black Swan and The Neon Demon are both set in a competitive, feminine environment - ballet and modeling. The younger, hungrier and more unique, the more successful they are. Black Swan is told from the perspective of the girl who is getting rejected only to finally land her big break, meanwhile The Neon Demon has all those girls getting rejected in the background on the story, focusing on young girl who arrives on the scene and instantly gets noticed.
Both films employ mirrors, injuries, surrounding the innocent girl with predatory male figures, trippy club scenes, girls lusting after other girls and possible possession angle.
Most of these are kinda straightforward but I also included some stuff like the prince who transforms into the evil sorcerer standing behind Nina and Jesse in front of that triangle after which her attitude changes (possible possession), blurred vision shot with Nina in the bathtub and Jesse in her last moments, red and teal tone dominating the final moments of both heroines' lives and the fact that the director shows us the last thing they both see before they die - well second to last for Jesse being the night sky and the reflectors shining bright for Nina.
(click to enlarge)