A few things to consider here:

At what point is a marriage not a marriage? You can legalize polygamy, but if you were to marry every other human being on the planet, does that still count as a marriage?

How long does it take to carry out a marriage and a divorce? Does it count if you are only married for one minute? What about one millisecond? Do you need a ceremony and paperwork? Does the data need to be recorded somehow?

In the most permissive case, I think we could literally get to infinity divorces per year. Imagine the law assigns every person a place in a finite list, and every day everyone's previous marriages (to Person[i]) are subject to divorce, and they are remarried to Person[i+1] (indices wrap around if greater than the length of the list). In theory this requires no actual paperwork or computation; if you want to know who you are married to, simply figure out what day it is and Person[Day%Person.length] is your spouse, but this was already the case even before you calculated it because the law says so.

Now change the amount of time between the recurring divorce/remarriage event to zero instead of one day. Infinite divorce.

On the other hand I think it's more reasonable that to be married to someone you have to at least kiss them, and that probably takes like ten seconds, so if we can get the human population up to 10 billion and get robots to support our basic needs while we spend our lives getting married, that's 6x60x24x365x10,000,000,000 = 31 quadrillion divorces a year, unless I did the math wrong which is likely.

Edit: forgot to consider that there would only be half as many divorces as people, so just cut that estimate in half