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We study the Markovian dynamics of a collection of n quantum systems coupled to an irreversible environmental channel consisting of a stream of entangled qubits. Within the framework of repeated quantum interactions, we derive the master equation for the joint-state dynamics of the n quantum systems. We investigate the evolution of the joint state for two-qubit environments where the presence of antidiagonal coherences in the state of the bath qubits (in the local energy basis) is essential for preserving and generating entanglement between two remote quantum systems. However, maximally entangled bath qubits, such as Bell states, exhibit exceptional behavior, where the master equation does not have a unique steady state and can destroy entanglement between the systems. For the general case of n-qubit environments we show that antidiagonal coherences that arise from multibody entanglement in the bath qubits do not affect the composite system evolution in the weak-coupling regime.