Shut off new immigration to nations that offer dual citizenship. Disqualify current immigrants from those nations from future American citizenship.
As you may (or may not) be aware, America is almost unique in that we allow non-citizens to own land and houses. There are people here, who work hard and pay taxes and own businesses (raise families, go to chruch, blah, blah, blah), yet have dual citizenships. If they renounce their dual citizenship status, they forfeit land from thier home country that have been in their family for generations. So, they will have a choice; forfeit their family's farm, businesses, home, and lands or leave America. That is unfair.
For example, I work with an engineer from India who is married to an American woman and is raising two children. His family owns considerable amounts of land in India. He is here legally, works hard, has bought a home and is legally pursuing the dual citizenship registration. He pays taxes like anyone else, he just gets to pay both US taxes, as well as taxes on his assets in India as well.