User authorization-based access privileges are a key feature in many safety-critical systems, but have not been extensively studied in the large language model (LLM) realm. In this work, drawing inspiration from such access control systems, we introduce sudoLLM, a novel framework that results in multi-role aligned LLMs, i.e., LLMs that account for, and behave in accordance with, user access rights. sudoLLM injects subtle user-based biases into queries and trains an LLM to utilize this bias signal in order to produce sensitive information if and only if the user is authorized. We present empirical results demonstrating that this approach shows substantially improved alignment, generalization, resistance to prefix-based jailbreaking attacks, and ``fails-closed''. The persistent tension between the language modeling objective and safety alignment, which is often exploited to jailbreak LLMs, is somewhat resolved with the aid of the injected bias signal. Our framework is meant as an additional security layer, and complements existing guardrail mechanisms for enhanced end-to-end safety with LLMs.