Design a parking garage (or an elevator bank, or chess). The low-level design round.

This round exists at Palantir for a reason that is not obvious from the prompt: modeling a customer's world into objects, links and actions is the daily work, so a candidate who produces a tidy but lifeless class diagram is showing you exactly how their ontology work will go. The two things scored hardest are whether you state an invariant and say where it is enforced, and what you do when two cars want the last space at the same moment. Everything else is vocabulary.