Douglas Harper's Etymology Dictionary
muck-a-muck
"(self-)important person," 1912, from Chinook jargon, literally "to eat; food." Also mucky-muck; muckety-muck.
Wiktionary
muck-a-muck
n. (alternative form of muckamuck English)
Usage examples of "muck-a-muck".
Playing the high and mighty lady muck-a-muck around here is going to get you nowhere, he blustered.
One of the big muck-a-mucks from the other side of the water had decided to make economies.
After all, you're gonna be showin off for some high muck-a-mucks tonight.