Normally, the Constitution's references to "the King" are interpreted as "the King and Government", or, more bluntly, "the Government, with the King rubber-stamping its decisions".
This is the case in most European monarchies.
For example, the Constitution states that the King appoints the Prime Minister (Article 12), but in practice the King appoints whomever politicians have chosen as Prime Minister based on the results of elections and party negotiations.
The Constitution
lovdata.no
However, when Crown Prince Haakon was engaged to marry Mette-Marit Tjessem Høiby, King Harald V claimed that for marriage approval (Article 36) only, "the King" should be interpreted as "Harald personally".
The then prime minister Jens Stoltenberg acquiesced to that dubious constitutional interpretation.
See
@ROYAL NORWAY's post here for details:
:previous: I don't know "for sure" but the components of the tiara date back to Queen Victoria's time so I don't think that Queen would give her son carte blanche. I tend to think that the Queen had a hand in it because other jewels that have been created on QEII's watch ranged from meh to...
www.theroyalforums.com
So I would say there is no need for an amendment, just for the King to give up his arbitrary, illogical interpretation of Article 36 of the Constitution, or for a Prime Minister to put their foot down and insist that "the King" in Article 36 means the same thing as "the King" in every other place in the Constitution.
Regardless of how good they may be as consorts, I don't think all of the listed spouses were vetted. Daniel Westling certainly wasn't: The King of Sweden only notified the Prime Minister Fredrik Reinfeldt of the engagement immediately before the announcement, and the prime minister signed his approval immediately afterwards, treating it as a mere formality.
ETA: Perhaps I should move this to
Opposition to Royal Marriages ?