The phrase "deep-seated" is often used to describe something that is firmly established or deeply ingrained. Some synonyms for this phrase include "inherent," "intrinsic," "fundamental," "underlying," and "ingrained." These words all convey a sense of something that is deeply ingrained or deeply rooted, whether it's a feeling, belief, or behavior. Other synonyms that can be used in place of "deep-seated" include "entrenched," "rooted," "fixed," and "unchanging." Using these synonyms can help readers to better understand the depth of something, and convey a sense of permanence or solidity that may be difficult to achieve with other wording.