When it comes to engaging with someone in a conversation, there are plenty of synonyms to choose from. For example, you could say that you want to "strike up" a conversation, "initiate" one, "start chatting" or "commence a discussion." On the other hand, if you're looking to continue a conversation that has already started, you might use phrases like "carry on" or "pick up where we left off." Additionally, there are more casual options like "shoot the breeze" or "chit-chat," or more formal phrases like "engage in dialogue." Regardless of the words you choose, the most important thing is to communicate effectively and respectfully in any conversation.