The mishna on Sanhedrin 21a teaches us that a king may not have more than 18 wives, and this is also codified by The Rambam (Hilchos Malachim 3:2):
לֹא יַרְבֶּה לוֹ נָשִׁים. מִפִּי הַשְּׁמוּעָה לָמְדוּ שֶׁהוּא לוֹקֵחַ עַד שְׁמוֹנֶה עֶשְׂרֵה נָשִׁים בֵּין הַנָּשִׁים וּפִלַּגְשִׁים הַכּל שְׁמוֹנֶה עֶשְׂרֵה
"He must not have too many women" (Deut. 17:17). By Tradition we have learned that he may have up to eighteen women including wives and concubines.
Now if a king were to marry a 19th wife:
- Would we say the kiddushin isn't valid?
- If it is valid, do we make him divorce her?
- Does the king get a punishment?