Luther insisted that whatsoever was not specifically forbidden by Scripture was optional for the Christian, and not only is there no Biblical ban on polygamy, there are positive examples of it, in the patriarchs. In January of 1521 … Luther had written to a friend whose marital life was wholly asexual owing to the illness of his wife and who had been asked whether he might take a second wife … Luther had responded that he could raise no objection if a man wished to take several wives, since Holy Scripture does not forbid it.

William Graham Cole
Sex in Christianity and Psychoanalysis
Oxford University Press, 1955, p. 116-117

Luther was consulted by a man whose wife … was unable to fulfill her marital obligation. The man felt himself unable to sustain the burden of chastity, and asked for Luther’s advice. Luther replied that … [he should] take a second wife. Luther … exhorted him to provide sufficiently for his first wife and not abandon her.

Raymond J. Lawrence, Jr.
The Poisoning of Eros: Sexual Values in Conflict
Augustine Moore Press, 1989, p. 178

I confess, indeed, I cannot forbid anyone who wishes to marry several wives, nor is that against Holy Scriptures …

Martin Luther
Cited by:
– Robert Hutchins, Multiple Marriage: A Study of Polygamy in Light of the Bible, 1987, p. 64.
– Philip Leroy Kilbride, Plural Marriage for Our Times, 1994, p. 63