Yes. Dual citizenship for Americans is not illegal nor is multiple citizenship in your case. But if you become a US citizen you must only furnish your US passport when you enter or leave the country.
“I hereby declare, on oath, that I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty of whom or which I have heretofore been a subject or citizen…”
The opening lines of the Oath of Allegiance are meant to give the United States exclusive sovereignty over the newly naturalized citizen. In other words, you are a citizen of one and only one country, the United States of America. The idea is that as soon as you take the Oath of Allegiance and become an American, you are giving up your citizenship of your native country.
Naturalized citizens are not legally obligated to give up their citizenship of their native country. The United States has never ordered (as far as we know) any newly naturalized US citizens to present themselves to their native country’s embassy and formally renounce their original citizenship. In the past, the first part of the oath was never a problem because almost all countries took away a person’s citizenship as soon as they became a citizen of another country.
Legally speaking, however, there is nothing in the Constitution and there are no past rulings from the United States Supreme Court preventing the United States (via the USCIS and the State Department) from requiring all naturalized citizens to officially renounce their original citizenship to their native country as a condition of naturalization.