Counterordering is a term used to describe the act of reversing or changing the order of something. The antonyms for counterordering would include words like maintaining, preserving, keeping, or maintaining the original order. Another antonym could be organizing, which would involve putting things in a specific order or following a predetermined sequence. Additional antonyms might include arranging, systematizing, sorting, or categorizing, all of which suggest a certain method or organization to the way things are done. Ultimately, the antonyms for counterordering would all involve maintaining a certain structure or order, and would be the opposite of changing or reversing the order in any way.