Stamping down refers to an act of forcefully crushing or suppressing something. There are several synonyms for this term, including "squash," "flatten," "subdue," "quell," "repress," and "smother." Squashing refers to compressing or crushing something down, while flattening involves pressing something to a flatter position. Subduing refers to reducing the intensity of something, while quelling means bringing something under control or suppressing a rebellion. Repressing involves suppressing a feeling or thought, while smothering refers to suffocating something or putting an end to it completely. All these synonyms convey the same meaning as "stamp down" and can be used interchangeably based on the context.