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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 been together form a verb phrase but should and have in this example are helping verbs that help the linking verb been, or should have been together can be all helping verbs like when you use it like this: He should have been running this morning but he couldn't get out of bed early enough.