To swarm over or cover something in large numbers.
From prefix 'be-' + 'swarm' (from Old English 'swearm'). The prefix intensifies the base verb to mean 'to cover completely with a swarm.'
The 'be-' prefix often created verbs describing complete coverage or overwhelming action — 'beswarm' would mean not just that bees were present, but that they were everywhere, completely covering an area.
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