As I showed previously under the discussion of concubinage in the BoM, the BoM speaks of the abomination of concubinage with specific focus on Solomon and David.
It is therefore important to realize that this cannot have meant polygamy in the general sense--Abraham and Jacob practiced that as well, and are not scorned for doing so. Abraham had one wife, Sarah, and two concubines, Hagar and Keturah (Adam Clarke's commentary to 1 Kings 11:3).
Rather, it must be in reference to the fact that Solomon was "tricked" into worshipping other gods than JHWH by his association with some of the other foreign princesses that he was married to (for diplomatic reasons, as we would argue today).
The key passage is 1 Kings 11, which tells how Solomon loses the kingdom. Historically speaking, this is a necessity; as the United Monarchy of David and Solomon is an invention of the Dtr Historians in the time of Josiah's cultic reform (cf. Israel Finkelstein, The Forgotten Kingdom, 2013), the monarchy cannot persist past the life of Solomon, otherwise the reality of the separated states of Judah and Israel cannot be connected to.
Whether this approach belongs to the revision under Ezra and Nehemiah, or is part of the Dtrn Historian, is unclear, but instituting a sin that involves the marriage of Solomon to foreign women is a masterful stroke of theological authorship. A quick look at the parallel passages --- Exodus 34:16; Deuteronomy 17:17; Ezra 10:44; Nehemiah 13; various passages in Proverbs, most of them concerned with adultery --- shows the focus on worship in the Pentateuch and the focus on flat-out marriage in Ezra and Nehemiah.
Of course the passage in 1 Kings dates the whole section to the 7th century, because the countries mentioned --- Moabites, Ammonites, Edomites, Zidonians, and Hittites --- include peoples that had not reached statehood until the 7th century (cf. Finkelstein 2013). In the case of the Hittites, the Separation Hypothesis suggests that these are similarly named hill tribes, not the big Anatolian kingdom of the 1600-1200 BC and its successor states.
The insertion had been done somewhat artless in the sense that 18th century commentators wondered why Solomon had only fallen under the theological spell of "Ashtoreth the goddess of the Zidonians", and "Milcom the abomination of the Ammonites", "Chemosh, the abomination of Moab", "Molech, the abomination of the children of Ammon", but not under the spell of the wife associated with his most crucial ally, the Egyptian princess. Some commentators went so far as to assume that she might have converted to Judaism; cf. Adam Clarke's rebuttal of that notion in commentary for 1 King 11:1.
Commentators had rejected the assumption that it was lust on the number of the women involved---700 princesses, 300 concubines---and on the age of Solomon; rather that he was collecting trophy wives the way that he was collecting horses and chariots, gold and silver.
The claim of desiring other women is an allusion to David and Bathsheba, the wife of Uriah (2 Samuel 11-12), and the mother of Solomon. But even here only the first child died; the second became as mentioned Solomon, the beloved of the LORD.