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So don't worry so much about how to use  had had  as a unit of grammar, they will come together naturally when you want to express the verb ' to have ' in the past perfect. Let's consider a different verb for a moment like  to want .
Should, have = auxiliary verbs; been = past participle; eating = present participle. A verb can have as many as four parts. When you form multipart verbs, you use a combination of auxiliary verbs and participles.