Comment by agalunar

Sure! Using "had been" rather than "(has) been" indicates that something may no longer be the case, e.g. "she's been well (and still is)" versus "she had been well (but is not necessarily still well)". So in my example

  She must've been being watched.

suggests that, at that point in the security footage, she might still be being watched. If the detective had said

  She must have had been being watched.

it would additionally imply that, at that point in the security footage, she was no longer being watched (but had been). So let me rework the story a bit:

  Two detectives are watching security film.

    DETECTIVE 1
  She's acting ordinarily, but I see fatigue written on her face. I wonder why.

  Detective 1 leans back in their chair and muses.

    DETECTIVE 2
  She must've had been being watched. The state security service monitors high-profile civilians occasionally, and a few days before this she was acting very cautiously, almost as if she was suspicious of something.

(Also, I think I falsely portrayed the universality of such a construction. Although I think some native English speakers would accept it as grammatical, many might not!)