Large scale data management systems utilize State Machine Replication to provide fault tolerance and to enhance performance. Fault-tolerant protocols are extensively used in the distributed database infrastructure of large enterprises such as Google, Amazon, and Facebook, as well as permissioned blockchain systems like IBM's Hyperledger Fabric. However, and in spite of years of intensive research, existing fault-tolerant protocols do not adequately address all the characteristics of distributed system applications. In particular, hybrid cloud environments consisting of private and public clouds are widely used by enterprises. However, fault-tolerant protocols have not been adapted for such environments. In this paper, we introduce SeeMoRe, a hybrid State Machine Replication protocol to handle both crash and malicious failures in a public/private cloud environment. SeeMoRe considers a private cloud consisting of nonmalicious nodes (either correct or crash) and a public cloud with both Byzantine faulty and correct nodes. SeeMoRe has three different modes which can be used depending on the private cloud load and the communication latency between the public and the private cloud. We also introduce a dynamic mode switching technique to transition from one mode to another. Furthermore, we evaluate SeeMoRe using a series of benchmarks. The experiments reveal that SeeMoRe's performance is close to the state of the art crash fault-tolerant protocols while tolerating malicious failures.