I have read enough history to know that the kings of England basically practiced polygamy. Mistresses. There is lists of illegitimate children for Henry I, Henry II, Edward II, etc.
But was polygamy practiced by anyone else? Even unofficial relationships?
I wouldn't call those polygamy, as polygamy refers to multiple spouses, not mistresses and concubines. If we're expanding it to mistresses and concubines, then the practice was quite widespread in Europe during the medieval period and beyond, with many Kings having multiple illegitemate children, although it depended on the specific king. Again, there's a difference between having lots of mistresses and concubines and having actual polygamy.
In England I believe you could a have a marriage without paperwork/authority. It was called a Danish marriage. These kings and lords had side chicks that they kept for a lifetime and fathered children with. At what point is it polygamy?
P.S.
I would have had a family in every castle, if I was the king. The wars can start when I die.