In hybrid- or multi-cloud systems, security information and event management systems often work with abstract level information provided by the service providers. Privacy and confidentiality requirements discourage sharing of the raw data. With access to only the partial information, detecting anomalies and policy violations becomes much more difficult in those environments. This paper proposes a mechanism for detecting undesirable events over the composition of multiple independent systems that have constraints in sharing information because of security and privacy concerns. Our approach complements other privacy-preserving event-sharing methods by focusing on discrete events such as system and network configuration changes. We use logic-based policies to define undesirable event sequences, and use multi-party computation to share event details that are needed for detecting violations. Further, through experimental evaluation, we show that our technique reduces the information shared between systems by more than half, and we show that the low performance of multi-party computation can be balanced out with concurrency-demonstrating an event rate acceptable for verification of configuration changes as well as other complex conditions.