You might also like Chungking Express, from Wong Kar-wai. It is a 90′s Hong Kong film with a similar atmospheric mood, three stories interwoven and not together, beautiful cinematography, and memorable characters. It’s mainly a love story, and a why-are-we-here story.. it’s also a comedy/drama.
Fallen Angels from the same director is similarly three parts that meet but don’t. This time about a hitman. Both of these films would complement the tone of Jarmusch.
Tarantino is a big fan of this director.
Of course Jarmusch always seems to get great fringe singers in his movies, and who can forget The Way of the Samurai… awesome,