If your dental office is recommending 3-4 cleanings a year and you have dental insurance that covers two, there is a good chance that they may cover more. My Delta Dental (a popular dental plan in the US) lets you add a free* rider via the website to cover four cleanings a year. It has a menu of medical reasons for the extra coverage from which you choose one.

I'm told diabetes and maternity are the most common reasons people access the additional cleanings.

* I realize this is priced into the default premiums.