USCIS will only recognize your first marriage as a valid marriage for immigration purposes. With that, you do not need to disclose marriages that take place after a first marriage is still legally valid. However, talk to an experienced immigration attorney if you have engaged in a marriage ceremony while you are legally married because you may be committing a crime in certain US states and in countries outside of the US. If you plan to practice, or have practiced, polygamy in the US or have attempted to be polygamous in the US, you will not be eligible for a green card.
If you need to talk to an experienced immigration attorney. We’ve helped hundreds of people traverse the complicated immigration and citizenship process. We would love to help you as well. Call (617-272-7980) or email email@example.com to get in touch.