The word "exterminatory" is used to describe something that seeks to eradicate completely. When we talk about something that is even more exterminatory, we mean to convey an even stronger sense of destruction. Synonyms for "more exterminatory" include devastating, lethal, annihilating, ruinous, catastrophic, catastrophic, and fatal. Each of these words denotes a sense of extreme lethality and harm that would lead to total destruction. They are all appropriate words to convey the idea of something that seeks to destroy completely. When faced with a situation that requires a description of destructive forces, one can easily substitute "more exterminatory" with any of these words and communicate the intended meaning effectively.