Polygamy can be defined as a marriage which includes more than two partners.
Polygamy in Westeros
The First Men
King Garland II "The Bridegroom" Greenhand, King of the Reach in the time before the Andals came to Westeros, had multiple wives. In order to marry the daughter of Lord Lymond Hightower, Lord of Oldtown, he put aside his other wives. This union, combined with the marriage of Lord Lymond and King Garland's daughter, brought Oldtown into the kingdom of House Gardener.
Lord Aenar Targaryen took multiple wives with him when he left Valyria for Dragonstone. His descendant, King Aegon I Targaryen, took to wife both his sisters, Visenya and Rhaenys. This was unusual, as per tradition he was expected to wed only his older sister, but not without precedent. It was said by some that Aegon wed Visenya out of duty and Rhaenys out of desire.
During the Conquest, Aegon received a proposal from the Storm King, Argilac Durrandon, who offered his daughter Argella as a wife to Aegon. Stating he did not need a third wife, Aegon refused the suggestion. Queen Regent Sharra Arryn of the Kingdom of Mountain and Vale offered herself in marriage to Aegon, but Aegon refused her offer as well.
Aegon I's younger son, Maegor, is the last Targaryen currently known to have had multiple wives. He had been married to Lady Ceryse Hightower in 25 ᴀᴄ, but in 39 ᴀᴄ, he took Alys Harroway to wife in a Valyrian ceremony led by his mother, Dowager Queen Visenya Targaryen, after they could not find a septon to perform the marriage. This marriage upset the Faith, especially the High Septon. When Maegor refused to set Alys aside, King Aenys I Targaryen sent them into exile in Pentos.
When Aenys died in 42 ᴀᴄ, Maegor returned from Pentos, and a courtesan named Tyanna arrived not much later, together with Queen Alys. Maegor took Tyanna to wife that same year. In 45 ᴀᴄ, Maegor's first wife, Ceryse, died due to sudden illness. Two years later, Maegor married his three Black Brides, widowed women of proven fertility, in a single ceremony.
With the death of their dragons during and after the Dance of the Dragons, House Targaryen saw a decrease in their power and threat that they needed to be able to get away with committing the sin of polygamy in Westeros. According to George R. R. Martin,
Maegor the Cruel has multiple wives, from lines outside his own, so there was and is precedent. However, the extent to which the Targaryen kings could defy convention, the Faith, and the opinions of the other lords decreased markedly after they no longer had dragons. If you have a dragon, you can have as many wives as you want, and people are less likely to object.
Despite the lack of dragons, it is possible that King Aegon IV Targaryen promised his bastard son Daemon Blackfyre that he could marry both Rohanne of Tyrosh and Aegon's daughter Princess Daenerys. King Aegon's successor, King Daeron II Targaryen, however, did not permit the second marriage.
There has been no mention of a Targaryen or Valyrian woman ever having more than one husband at a time. Nonetheless, in 299 ᴀᴄ Ser Jorah Mormont proposes the idea to Queen Daenerys Targaryen as a possible meaning for "the dragon has three heads", a phrase that Daenerys had heard in her visions at the House of the Undying. Daenerys speaks of the possibility to Prince Quentyn Martell a year later, suggesting that her marriage to Hizdahr zo Loraq need not be the end of Quentyn's hope to marry her, but his adverse reaction to her dragons causes her to dismiss the idea.
The Iron Islands
On the Iron Islands, a man can have one true- and freeborn "rock wife". However, he can also have "salt wives", usually women captured on raids. Salt wives are considered more than mere concubines, and any sons born of such unions are not considered bastards, but can inherit should their father have no surviving sons by his rock wife. The number of salt wives a man can support is considered to be an indication of his power, wealth, and virility.
In Dorne, it is not uncommon for a nobleman or a noblewoman to have a spouse for political reasons and a paramour for love. While the Dornish are not very concerned if a child is born out of marriage, children by paramours are nevertheless considered to be bastards, and thus have to use the surname "Sand", while the children by the spouse use the family name and inherit.
In the era of King Jaehaerys I Targaryen, there was a Kingsguard knight named Ser Lucamore Strong, called "Lucamore the Lusty", who had three wives and sixteen children. Knights of the Kingsguard are not allowed to have wives or children, so when Lucamore's deceit was discovered, his own brothers of the Kingsguard gelded him, and the king sent him to the Wall.
Polygamy in Essos
- Wikipedia: Polygamy
- The World of Ice & Fire, The Iron Islands.
- The World of Ice & Fire, The Targaryen Kings: Aenys I.
- The World of Ice & Fire, The Reach: Garth Greenhand.
- The World of Ice & Fire, The Reach: The Gardener Kings.
- The World of Ice & Fire, The Reach: Oldtown.
- The World of Ice & Fire, The Stormlands: House Durrandon.
- The World of Ice & Fire, The Reign of the Dragons: The Conquest.
- The World of Ice & Fire, The Targaryen Kings: Maegor I.
- The Sons of the Dragon.
- So Spake Martin: Asshai.com Forum Chat (July 27, 2008)
- The World of Ice & Fire, The Targaryen Kings: Daeron II.
- A Storm of Swords, Chapter 8, Daenerys I.
- A Clash of Kings, Chapter 48, Daenerys IV.
- A Dance with Dragons, Chapter 50, Daenerys VIII.
- A Clash of Kings, Chapter 11, Theon I.
- The World of Ice & Fire, Dorne: Queer Customs of the South.
- A Clash of Kings, Chapter 23, Jon III.
- A Dance with Dragons, Chapter 69, Jon XIII.
- A Feast for Crows, Chapter 13, The Soiled Knight.
- A Clash of Kings, Chapter 10, Davos I.
- A Storm of Swords, Chapter 54, Davos V.
- A Game of Thrones, Chapter 46, Daenerys V.
- The World of Ice & Fire, Beyond the Free Cities: Ib.
- A Storm of Swords, Chapter 71, Daenerys VI.
- A Clash of Kings, Chapter 63, Daenerys V.
- The World of Ice & Fire, The Bones and Beyond: Yi Ti.
- The World of Ice & Fire, The Bones and Beyond: Leng.