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Automatic speech recognition (ASR) training can utilize multiple experts as teacher models, each trained on a specific domain or accent. Teacher models may be opaque in nature since their architecture may be not be known or their training cadence is different from that of the student ASR model. Still, the student models are updated incrementally using the pseudo-labels generated independently by the expert teachers. In this paper, we exploit supervision from multiple domain experts in training student ASR models. This training strategy is especially useful in scenarios where few or no human transcriptions are available. To that end, we propose a Smart-Weighter mechanism that selects an appropriate expert based on the input audio, and then trains the student model in an unsupervised setting. We show the efficacy of our approach using LibriSpeech and LibriLight benchmarks and find an improvement of 4 to 25% over baselines that uniformly weight all the experts, use a single expert model, or combine experts using ROVER.