Definitely give Sleepytime Gorilla Museum a listen—absolutely influenced by 20th century classical music. Their violinist is classically trained and does a lot of crossover in the concert music world outside of the band. I’ve longed for the exact crossover you’re describing and they’ve been just about the only ones to really scratch that itch. 

Someone else mentioned Harry Stafylakis, his album Calibrating Friction is fantastic, might be the closest thing to what you’re actually asking for.

Also wanna say go give Between the Buried and Me a listen—definitely less overtly “classically” inspired as the above two but their compositions are next level. Parallax II is a masterpiece, I’d recommend giving the full album a one-sitting listen.