My great great grandfather, Niels Hansen Jensen, lived in Utah in the 19th century and had two wives. My great great grandmother, Nicolena Rolfsen, was his first wife. He married her in 1868. Together they had one daughter, who died in infancy. In 1884, Niels took Sarah Fechser as his second wife. According to family history, it was Brigham Young himself who suggested that Niels take another wife, due in part to the fact that Niels and Nicolena were childless (see http://lythgoes.net/genealogy/history/NielsJensen.php).
Also according to the same family history, Niels was sent on a mission to Denmark after the second married, apparently in an effort to escape the federal agents who were cracking down on plural marriages.