"Go the rounds" is an idiom that means to circulate or make a circuit, especially in a systematic way. There are several synonyms for this phrase, such as "circulate," "spread," "travel," "move around," "relay," "pass around," and "make the rounds." These words signify the act of something or someone being passed from one person to another or around a particular place. They all embody the idea of moving from one place to another in an organized and methodical way. Hence, to communicate the idea of something being widespread or making the circuit, any of these synonyms can be used interchangeably with the phrase "go the rounds".