The phrase "push aside" can be replaced with various synonyms depending on the context and tone of the sentence. Some common synonyms include "set aside," "brush off," "disregard," "ignore," "overlook," and "shove aside." "Set aside" implies that the subject is temporarily putting something aside for later consideration. "Brush off" and "shove aside" suggest a more forceful manner of disregarding something. "Disregard" and "ignore" are more neutral options implying a lack of attention or consideration. "Overlook" has a similar meaning, but could also suggest a mistake or oversight in not giving something enough attention. These synonyms allow for variations in language and tone, allowing writers and speakers to precisely express their thoughts and intentions.