Modern distributed, object-based systems support nested method invocations, whereby one object can invoke methods on another. In this paper we present a framework that supports nested method invocations among Byzantine fault-tolerant, replicated objects that are accessed via quorum systems. A challenge in this context is that client object replicas can induce unwanted method invocations on server object replicas, due either to redundant invocations by client replicas or Byzantine failures within the client replicas. At the core of our framework are a new quorum-based authorization technique and a novel method invocation protocol that ensure the linearizability and failure atomicity of nested method invocations despite Byzantine client and server replica failures. We detail the implementation of these techniques in a system called Fleet, and give preliminary performance results for them.