Is polygyny without a clear and explicit reason permissible or forbidden in Islamic law, taking into account the potential destruction this polygyny might cause to the first household?

For polygyny to be permissible, physical and financial capability, as well as justice, are required. It is also important to note that the husband is religiously obligated to be gentle with his first wife and persuade her when considering polygyny. The natural jealousy of a woman is not considered a corruption that outweighs the numerous benefits of polygyny, which Allah has legislated out of His knowledge of His servants' interests. It has many wisdoms, including:

Closing the door to adultery given the greater number of women than men. Providing comfort and a home for women who cannot find a husband, and enabling them to have offspring. A fair view towards all women (spinsters, widows, and unmarried women). Polygyny is not obligatory; it is for those who are capable of it and need it. The difference in the physical nature of women compared to men, which makes them not always ready for intimacy. The possibility of marrying another woman in case of the first wife's infertility or bad conduct, without divorcing her. A man's reproductive capacity is greater than a woman's. Polygyny may provide relief to the first wife from marital burdens. Gaining reward by marrying a needy woman who has no provider. The fact that Allah the Almighty is the One who permitted polygyny, and He knows best what is beneficial for His servants.