Reconfigurable state machine replication is an important enabler of elasticity for replicated cloud services, which must be able to dynamically adjust their size as a function of changing load and resource availability. We introduce a new generic framework to allow the reconfigurable state machine implementation to be derived from a collection of arbitrary non-reconfigurable state machines. Our reduction framework follows the black box approach, and does not make any assumptions with respect to its execution environment apart from reliable channels. It allows higher-level services to leverage speculative command execution to ensure uninterrupted progress during the reconfiguration periods as well as in situations where failures prevent the reconfiguration agreement from being reached in a timely fashion. We apply our framework to obtain a reconfigurable speculative state machine from the non-reconfigurable Paxos implementation, and analyze its performance on a realistic distributed testbed. Our results show that our framework incurs negligible overheads in the absence of reconfiguration, and allows steady throughput to be maintained throughout the reconfiguration periods.