US only allows naturalized US citizens to keep their non-USA citizenship. I have a friend who has Greek (his birth place), German (his parents moved to Western Germany), Canadian and USA passports.
But if you are born in USA then you are a US citizen by birth. If you want to obtain a citizenship of your residing country, you must go to the US embassy/Consulates by person to abandon your US citizenship before you are grandad a residing country citizenship. Otherwise, you violated US law and you will be in trouble at the US Customs if you rerun to USA no matter what kind of passport you use, unless you never go back to USA.