JohnMacWW

Excellent, thanks.
So they wrote:
"U.S. national may acquire foreign nationality by marriage, or a person naturalized as a U.S. national may not lose the nationality of the country of birth. U.S. law does not mention dual nationality or require a person to choose one nationality or another."
Thus what they say is that, while "nationality" is defined in U.S. law (Section 101(a)(22) of the Immigrationand Nationality Act (INA) there is nothing in the law about dual or even multi-nationality.
They also say that:
"In order to lose U.S. nationality, the law requires that the person must apply for the foreign nationality voluntarily, by free choice, and with the intention to give up U.S. nationality."
They do not give a citation to that, but I suspect it is right there in the INA also. Their discussion goes on talk about using passports etc, most with a discussion around whether or how one could express an "intention to give up U.S. nationality." That is what you want to avoid, I guess, when you have two nationalities (unless of course you want to rid yourself of your U.S. nationality).
Now that my wife has her Italian citizenship I am applying for mine (since I am married to an Italian.). This gives me comfort that I can do so without surrendering my U.S. citizenship. We will maintain residence, accounts, etc in both countries and, it seems to me that by entering and exiting the U.S. on your U.S. passport you are helping to express your continuing committment to comply with U.S. laws and, well, be an American.