Countries that allow dual CITIZENSHIP
In almost all circumstances, yes. You may be required to declare “other allegiances” when applying for certain government programs or a US passport, but their request is more snooping than anything else.
You should be aware that taking up a foreign citizenship with the “intention” of relinquishing your US citizenship can cause you to lose US citizenship. So can fighting in a foreign military or working for a foreign government in any number of jobs.