High muck a muck is a colloquial term to describe someone who holds a high-ranking position or possesses an air of superiority. Some synonyms for this phrase include highfalutin, pompous, haughty, snooty, pretentious, and egotistical. Other related words may include arrogant, conceited, and self-important. These terms all convey a sense of superiority or importance and can be used to describe someone who acts as if they are better than others. It's important to note, however, that these words are subjective and should be used carefully and with consideration for the individual in question.