The phrase "more deep down" can be replaced with a variety of synonyms depending on the context. To convey a deeper level of understanding or emotion, words like "profoundly" or "intensely" can be used. For a greater level of introspection or analysis, "further inward" or "more introspective" may be appropriate. Alternatively, if discussing a level of secrecy or hidden information, phrases such as "more covertly" or "beneath the surface" could be utilized. Overall, there are many synonyms available to accurately describe a deeper level of emotion, analysis, or hidden information.