Can I use the verb be in present perfect continuous tense or it is always stative?
Are there any exceptions?
Be has a slightly different meaning in continuous constructions: it means approximately behave:
He's a jerk. (he is a jerk all the time)
He's being a jerk. (he's behaving like a jerk right now)
There's no reason you can't employ this continuous sense in a present perfect construction:
He's been being a jerk ever since we got here.
However, you are more likely to encounter the same sense in an ordinary present perfect construction:
He's been a jerk ever since we got here.
The two perfect versions both have essentially the same meaning, because just like the present continuous they mark the state of jerkhood as temporary, and by inference a matter of current behavior rather than permanent character.