The phrase "more by the way" is often used to introduce additional information or thoughts to a conversation. Other phrases that can be used as synonyms for this phrase include "in addition," "furthermore," "moreover," and "additionally." These phrases are ideal for use in both casual and formal settings when you want to add more information to a discussion without disrupting the flow of the conversation. However, it is important to use these phrases sparingly, as too many additions can be overwhelming and distract from the main point of the conversation. Therefore, it is always good to be mindful of the flow of conversation when using such phrases.