"more than satisfied" is a correct and usable phrase in written English. It is typically used to compare levels of satisfaction between two things. For example, "I was more than satisfied with the results of the experiment.".
Some are more than satisfied.
The Faillaces declared themselves more than satisfied.
It more than satisfied my cravings, without emptying my wallet.
May will be more than satisfied with this.
After four hours, we were drained, but more than satisfied.
Rosberg was more than satisfied with his performance.
The woman did, and after her massage, Ms. Macnow said the more-than-satisfied customer apologized for grumbling.
Awesome tool! I started using it one year ago and I never had to look for another app
Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia