A very formal way of saying ''Eat my ass, eat yo ass, eat his/her ass, etc.'', the meaning is of course based on the context or phrasing of the sentence.
Example 1:
Teacher: "Bob! Don't put your legs on top of the table!"
Bob: "You can eat my ass."
Teacher: "Excuse me?! How dare you say that! Apologize this instant!"
Bob: "Oh, I am sorry, let me rephrase that, I am allowing you to consume thine buttocks."

Example 2:
Prince: "Oh princess, oh the dear one, the beauty of this kingdom, I have always wished to see you this close, and as close as a woman and a man can be. I have tastes that you might question but, will you allow me to consume thine buttocks?"
Princess: "The fuck... Nah, let's not..."
by CoffeeK_ November 26, 2018
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