To squeeze or compress something thoroughly; to press or crush from all sides.
From 'be-' (prefix) + 'squeeze' (to apply pressure). The prefix suggests complete or thorough compression from multiple directions.
Though rarely used, 'besqueeze' is delightfully logical—if 'besmear' means thoroughly smear, why shouldn't 'besqueeze' mean thoroughly squeeze? English word-formation can be productive, even if the word never becomes common.
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