Most countries allow dual citizenship. The USA doesn't. Canadians who become US citizens automatically retain Cnanadian citizenship too.
If you're Jewish, you can become a citizen of Israel as well as the USA.
If you can prove Italian ancestry, you can get an Italian passport.
Some countries allow you to buy citizenship, usually for $250,000 or so. But these seem to be tiny islands that no one ever heard of.
I'm surprised that some "real" country, like Canada, doesn't pass a law letting Americans have citizenship provided they pass certain criteria and invest a reasonable amount of money in Canadian businesses. The 1960s, when Pakistanis bought "tours" to Canada with one-way flights and US draft dodgers declared themselves landed immigrants, are long gone.
Whatever you do, do not renounce US citizenship. The US has a law that lets them confiscate most of your assets if you do.
I have a friend who bought a place in an 8000 person enclave of Americans and Canadians 35 miles from Guadalajara, the second largest city in Mexico. I would not move to Mexico no matter what.
