"High-muck-a-mucks" is a colloquial term that refers to people who hold high positions or have a lot of influence. However, there are alternative phrases that can be used to describe such individuals. One option is "bigwigs," which also conveys a sense of power and importance. "Movers and shakers" is another term commonly used to refer to people who have a lot of influence in the business world or in politics. "Power players" is also a phrase that can be used to describe high-ranking individuals. Ultimately, there are many different synonyms for "high-muck-a-mucks" that can be used depending on the context and tone of the conversation.