No, you cannot legally marry a man and a woman at the same time in the United States.
The act of marrying more than one person is known as polygamy. Polygamy is illegal in every state in the United States. The Edmunds Anti-Polygamy Act of 1882 explicitly outlawed the practice.
Essentially, marriage in the US legal system is designed as a union between two people at any given time. Attempting to marry multiple people simultaneously would be considered a criminal act.
