This paper addresses the monitoring of logic-independent linear-time user-provided properties on multi-threaded component-based systems. We consider intrinsically independent components that can be executed concurrently with a centralized coordination for multiparty interactions. In this context, the problem that arises is that a global state of the system is not available to the monitor. A naive solution to this problem would be to plug a monitor which would force the system to synchronize in order to obtain the sequence of global states at runtime. Such solution would defeat the whole purpose of having concurrent components. Instead, we reconstruct on-the-fly the global states by accumulating the partial states traversed by the system at runtime. We define formal transformations of components that preserve the semantics and the concurrency and, at the same time, allow to monitor global-state properties. Moreover, we present RVMT-BIP, a prototype tool implementing the transformations for monitoring multi-threaded systems described in the BIP (Behavior, Interaction, Priority) framework, an expressive framework for the formal construction of heterogeneous systems. Our experiments on several multi-threaded BIP systems show that RVMT-BIP induces a cheap runtime overhead.