There are many synonyms for the phrase "turn something upside down." Some of these include flip, invert, upend, reverse, and overturn. Each of these words conveys the idea of turning something over so that what was once on the top is now on the bottom, and vice versa. In most cases, these synonyms can be used interchangeably, as they all describe the same action. However, some may be more appropriate in certain contexts than others. For instance, "upend" may be better suited for describing the flipping of a heavy object, while "invert" may be better for describing the turning of a small, delicate item.