The term "more tertiary" generally refers to something that is more advanced or developed in a specific field or discipline. Synonyms for this phrase might include "higher-level," "advanced," "specialized," or "expert." Other related terms might include "graduate-level," "professional," or "specialist." Depending on the context, other possible synonyms for "more tertiary" might include terms like "cutting-edge," "innovative," "groundbreaking," or "pioneering." Ultimately, the most appropriate synonym will depend on the specific context in which the term is being used and the particular nuances of meaning that are associated with that context.