Co-op is never inflected because it is a noun (although it can function as an adjective). Both words are usually hyphenated to reflect pronunciation (and to prevent confusion with coop).
Co-op | Business English.
In this use, the word is often shortened to co-op.
Co-op is the short form for co-operative. Co-op (or Co-operative) housing is very popular in Sydney. Ian shops at a food co-op where he earns a membership dividend.
1. A cooperative name must contain the word “cooperative”, “coop”, or the abbreviation “CP”.
Two or more organizations combine their requirements and solicit bids or offers for goods or services. One or more organizations represent their requirements and include an option for other organizations to “ride” or “bridge” the contract as awarded.