Can dual be given during a passenger flight under part 91? Is there an FAR I can refer to concerning this issue?

Thanks

Define passenger flight? Can you conduct instruction with passengers onboard? Yes. But if I'm logging dual personally, the primary purpose of the flight should be for instruction.

Yes, you can. It's done all the time.

It can be a pleasure flight where the pilot brings along pax(s) and also an instructor to knock out a cross country or just for backup.

It can be a local training flight where the student's friend comes along just to observe.

You could also be doing a "revenue flight" in a jet with the owner on board and one pilot giving dual to the other along the way.

But there has to be a legit training purpose. You can't just log dual every time you get in an airplane.