It is true that ancient Greek sources dating to as early as the fourth century BCE claim that the Spartans had a custom wherein Spartiate men (i.e., men possessing full Spartan citizenship) could, in effect, loan out their wives to other Spartiate men for the purpose of producing offspring.

The ancient sources unanimously portray this as something that was only permitted if the woman's husband consented to it. Rather disturbingly from our modern perspective, the woman's own consent does not seem to have been important, since, in Sparta, women were owned by their husbands and the woman's husband's consent was apparently all that mattered.

The Athenian historian Xenophon (lived c. 430 – c. 354 BCE) writes in his On the Constitution of the Lakedaimonians 1.7–8, as translated by Richard J. A. Talbert:

“[The Spartan lawgiver Lykourgos] observed, however, that where an old man happened to have a young wife, he tended to keep a very jealous watch on her. So he planned to prevent this too, by arranging that for the production of children the elderly husband should introduce to his wife any man whose physique and personality he admired. Further, should a man not wish to be married, but still be eager to have remarkable children, Lykourgos also made it lawful for him to have children by any fertile and well-bred woman who came to his attention, subject to her husband’s consent.”

The later Hellenistic Greek historian Polybios of Megalopolis (lived c. 200 – c. 118 BCE) writes in his Histories 12.6b.8, as translated by W. R. Paton:

"For among the Lakedaimonians [i.e., the Spartans] it was a hereditary custom and quite usual for three or four men to have one wife or even more if they were brothers, the offspring being the common property of all, and when a man had begotten enough children, it was honourable and quite usual for him to give his wife to one of his friends."

The even later Greek biographer and Middle Platonist philosopher Ploutarchos of Chaironeia (lived c. 46 – after c. 119 CE) similarly gives an account of this practice in his Life of Lykourgos 15.6–7, writing, as translated by Bernadotte Perrin:

"After giving marriage such traits of reserve and decorum, he [i.e., Lykourgos] none the less freed men from the empty and womanish passion of jealous possession, by making it honourable for them, while keeping the marriage relation free from all wanton irregularities, to share with other worthy men in the begetting of children, laughing to scorn those who regard such common privileges as intolerable, and resort to murder and war rather than grant them."

"For example, an elderly man with a young wife, if he looked with favour and esteem on some fair and noble young man, might introduce him to her, and adopt her offspring by such a noble father as his own. And again, a worthy man who admired some woman for the fine children that she bore her husband and the modesty of her behaviour as a wife, might enjoy her favours, if her husband would consent, thus planting, as it were, in a soil of beautiful fruitage, and begetting for himself noble sons, who would have the blood of noble men in their veins."

Most historians that I am aware of accept that there is some historical reality underlying these reports. Paul Cartledge, one of the foremost historians of ancient Sparta alive today, argues in his paper "Spartan Wives: Liberation or License?" (published in 1981 in The Classical Quarterly, New Series, Vol. 31, No. 1, pp. 84–105) on pages 102–104, that some form of "what we might describe as plural marriage and polykoity" existed in ancient Sparta. He nonetheless cautions (on page 104):

"We cannot, however, say how frequent such liaisons may have been nor what psychological effect they may have had on Spartan wives - a salutary reminder of the inadequacy of the ancient evidence."

I personally agree that a system probably really existed in ancient Sparta in which it was possible for Spartiate men to loan out their wives to other men for the purpose of procreation, but we cannot say how common such a thing really was in practice.