Would it be legal to marry and divorce the same person as many times as possible?

Imagine a couple trying to set the record for being married and divorced the most times. As quickly as courtdates/marriage licenses allow, they legally marry and then immediately legally divorce. They do this over and over and over. The divorces are always totally amicable. Both parties are completely and honestly committed to the bit. They pay all filing fees.

Would anyone ever put a stop to this? It's a massive waste of time for the marriage license office and the divorce court, and I feel like a judge might eventually get annoyed, but would it be legal to bar someone from marrying whom they please or choosing to divorce if they wanted to?

I don't plan to try this because it's stupid and the filing fees would start to pile up. It's just a thought I had.