The phrase "brush by" means to come close to or pass by something or someone quickly and lightly. There are several synonyms for this phrase, including skim, glance off, graze, sidle past and whisk past. Each of these words emphasizes a specific aspect of the action, whether it's the speed of the movement or the lightness of the touch. Other related words that can be used as synonyms for "brush by" include nudge, rub against, touch upon and skim over, all of which suggest a fleeting or gentle contact with a surface or object. Overall, there are many ways to describe the act of brushing by something, each with its own connotations and nuances.