When looking for synonyms for "most deep-down," one can turn to phrases such as "most profound," "innermost," or "core." These terms all convey a sense of intensity and significance at the very essence or heart of something. Another option is "intrinsic," which emphasizes something being essential or inherent to the nature of something else. "Fundamental" can also be considered, describing something that is foundational or crucial to the structure of a system or concept. Ultimately, the right choice of words will depend on the specific context, but these options all capture the idea of something being deeply seated and important.