Legally, a man cannot have two wives at the same time in America. This would also apply to a man looking to have two husbands, or a woman trying to marry two people at once. However, if one wife dies, the man is free to remarry at his will. If he decides to divorce his first wife, he may marry a second wife. Same for a woman who has divorced or become widowed.
The only illegal thing about that situation would be if he tried to marry two wives at once. This is not a common practice in America, and it has been illegal since the 1800s. However, back when America first became a country, it was legal but still uncommon.