If you are curious about the US’s stance on dual-citizenship, you will be happy to know that, according to the US government, the US does not require a person to discard other citizenships for US citizenship.
There are still some rules attached to maintaining US citizenship. While you can have as many passports as you would like under US law, there are certain stipulations that you still must follow. For example, running for political office or serving in your home country’s army may cause you to lose US citizenship (though there are exceptions to this). Committing an act of treason against the United States may also mean the removal of your US citizenship.