dual citizenship, immigration, can a person get U.S. citizenship without giving up other countries citizenship

The US government generally no longer prohibits a US citizen from also being a citizen of other countries. As long as a US citizen does not commit one of the actions mentioned in INA Sec 349 (LOSS OF NATIONALITY BY NATIVE-BORN OR NATURALIZED CITIZEN), the US citizen likely would not lose US citizenship. The Immigration and Nationality Act can be accessed at www.uscis.gov .

My understanding is that some other countries do not allow their citizens to have multiple citizenship. If you now hold dual citizenship, you likely have already checked the laws of those countries. However, to be safe, you likely should check with those countries.