Secure multi-party cryptographic protocols divide the secret key among multiple devices and never reconstruct it in a single place. Such a mechanism protects against malware, code vulnerabilities, and backdoors when different implementations and devices are used. Still, a protocol-level issue may result in a compromise, and up until now, it has been unknown how to combine different unmodified multi-party protocols. We study the interoperability of different multi-party Schnorr signature schemes and classify them based on their approach to the nonce agreement. We identify issues that could hinder in-class interoperability, and we propose a trustless mediator that facilitates interoperability among different classes in certain cases. Besides mitigating the risks, interoperability provides usability and performance benefits, as protocols better suited for special devices can be used together with more general protocols. We make use of these advantages in our new multi-signature scheme SHINE, which is optimized for resourcelimited devices like cryptographic smartcards while being interoperable with popular schemes such as MSDL, MuSig2, or SpeedyMuSig.