Secure multi-party computation (MPC) enables (joint) computations on sensitive data while maintaining privacy. In real-world scenarios, asymmetric trust assumptions are often most realistic, where one somewhat trustworthy entity interacts with smaller clients. We generalize previous two-party computation (2PC) protocols like MUSE (USENIX Security’21) and SIMC (USENIX Security’22) to the three-party setting (3PC) with one malicious party, avoiding the performance limitations of dishonest-majority inherent to 2PC.We introduce two protocols, AUXILIATOR and SOCIUM, in a machine learning (ML) friendly design with a fast online phase and novel verification techniques in the setup phase. These protocols bridge the gap between prior 3PC approaches that considered either fully semi-honest or malicious settings. AUXILIATOR enhances the semi-honest two-party setting with a malicious helper, significantly improving communication by at least two orders of magnitude. SOCIUM extends the client-malicious setting with one malicious client and a semi-honest server, achieving substantial communication improvement by at least one order of magnitude compared to SIMC.Besides an implementation of our new protocols, we provide the first open-source implementation of the semi-honest 3PC protocol ASTRA (CCSW’19) and a variant of the malicious 3PC protocol SWIFT (USENIX Security’21).