As far as I'm aware, if you're a US citizen you're (ostensibly; enforcement is inconsistent as hell) subject to US laws (federal, at a minimum, and more depending on exact circumstances and jurisdiction) regardless of where you are. Extra citizen status(es) don't really factor into that much. Far as US law is concerned the US citizenship trumps everything else if they're wanting to drag your ass to court, occasional treaty or diplomatic agreement notwithstanding, and it's pretty damn rare any other country cares to argue too loudly about it. Trials in absentia are also a thing, so...
There's a long history of corporate kvetching over that, due to anti-corruption/bribery laws (theoretically) applying to US corps operating in other countries, even if basically everything involved in the particular operation was occurring outside US borders and not interacting with the US's direct economy or legal infrastructure much or at all. Lots of yelling about not being able to compete in corrupt foreign economies without being able to get involved in kickbacks and whatnot (narrator voice: their complaints are and always were horseshit, they just want to grift). Similar hooting and hollering involving taxation and sex tourism, iirc, occasionally stuff about medical tourism (particularly short hop stuff and prescriptions, if my memory's not short circuiting).
Short of it is there's a reason ex-pats renounce US citizenship sometimes. Folks often aren't particularly aware (or it's not relevant to their specific circumstances) that there's some pretty significant baggage attached to the benefits.