Depending on how modern of classic you are looking for, I’d add

Hitchhikers Guide to the Galaxy (late 70s) The Fellowship of the Ring (50s) Brideshead revisited (1945) And Then There Were None (1939) Phantom of the Opera (1910)

I also second The Picture of Dorian Gray, Virginia Woolf and The Amazing Adventures of Kavalier & Clay (it’s a 2000s book)