Going around with means to regularly spend time with someone in a romantic context or as close friends. There are many synonyms for this phrase varying in different levels of formality. Some of the common synonyms are "dating," "seeing each other," "going steady," "courting," "in a relationship," "partnered," "romantically involved," and "romantically linked." Other informal synonyms include "hooking up," "crushing on," "together," "exclusive," and "committed." Each of these synonyms has a slightly different connotation, so it's essential to choose the best one for the context. However, all of them imply a positive, close bond between two individuals.