No, the answer is to separate marriage into its secular and sacred dimensions, and to let the state administer the first while religious institutions administer the latter. Call the formal "civil marriages" if you must, but recognize that any religion is free to reject a mere civil union as a marriage for religious purposes.
When I was teaching in Turkey, I frequently passed a city building where marriages took place. Marriages were a purely civil matter, with registration with the city government being the only requirement. I asked my department chairman about religious weddings. He said that after the civil wedding, the couple could ask an Imam to come to their house and bless the marriage, but that wasn't required.
I do think some kind of civil registration is needed, because there must be records of who is already married, who is married to whom, who will be responsible for the care of children, who will inherit property, etc. Marriage is not a purely private affair. There are lots of ways in which society is involved in marriage, and that must be accounted for.
And the secular ones are called "partnerships." There are plenty of laws concerning the formation and dissolution of partnerships. I don't care if it has 20 people.
The state can neither make nor dissolve a marriage. The state does not have that capacity, regardless of the number of laws we pass. We can pass a law saying the Earth is flat, the universe is 2 Kilometers by 2 Kilometers, we're drinking free bubble up and eating our rainbow stew. That doesn't make it so. Popular opinion, even when put to a vote, does not govern the universe.