A person who is cooperating or being cooperated with; one involved in a cooperative arrangement or coop-like situation.
Formed from coop with the agentive suffix -ee (marking the recipient of an action), similar to payee, employee, or lessee. This is a relatively rare or informal formation.
The -ee suffix marks the person receiving an action (employee, interviewee, payee), so coopee would theoretically be the person being cooperated with—it's a word formation pattern English speakers understand intuitively, even if they rarely use this particular example.
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