The phrase "more deep-down" can be replaced with several synonyms depending on the context and tone of the sentence. Some alternatives include "more profound," "more visceral," "more ingrained," and "more intrinsic." These synonym choices can convey a greater sense of depth, emotion, and significance depending on the intended meaning of the sentence. For example, "more profound" suggests a greater intellectual or philosophical depth while "more visceral" implies a more intense physical or emotional experience. It is important to consider the context and intended tone when selecting a synonym to ensure the appropriate meaning is conveyed.