What are some multi-dimensional characters?

The Sound and the Fury - author: William Faulkner - Quentin! This is the best example I can think of. The man is a highly philosophical thinker that grapples with how pressing the issue of time is. He wished he had an incestuous relationship with his sister, because if something so awful could happen it might be able to transcend time because they are all mortal. He is obsessed with family honor and how the loss of his Southern family's standing is related to his sister's promiscuity. Her name is Caddy by the way. He ultimately kills himself, after one of the most amazing and powerful passages in U.S. literature. Benjy is one of her other brothers, who has a developmental disability and cannot recall memories chronologically. One memory reminds him of another and so on, so it's incredibly difficult to read and follow. Caddy is his only real caregiver, and he's constantly mortified to find out that she isn't there because he jumps from memory to memory, not recalling the sequence of events. Jason is her other brother, an alcoholic who emotionally abuses Caddy's daughter, and confiscates the money that Caddy sends to help support her. This guy is a real S.O.B.

The Great Gatsby - author: F. Scott Fitzgerald - Gatsby because he is focused on recreating the past with Daisy, he has built himself up from a simple midwestern existence, and he is a criminal. Daisy from the same book because she is bored with her socialite life, but frustrated with her husband's rampant philandering.

Slaughterhouse Five - Billy Pilgrim (the main character) is traumatized by witnessing the bombing of Dresden, he is simultaneously being considerate of his friends, developing his own possible madness, and coping with mortality.

i would say most of the characters from beloved (by toni morrison)

for ex. beloved is driven by two things: love for her mother and the desire to be loved in return and to enact revenge on her mother and kill her