"more and more often" is correct and usable in written English. It is most often used to indicate something that is happening with increasing frequency. For example, "We have been going to the beach more and more often lately."
The wife screamed more and more often.
But it's happening more and more often.
This seems to be happening more and more often.
Then, more and more, often, men will lose their machines.
Such talk is heard more and more often these days.
It is happening more and more often, she said.
"People are eating more, and more often," Dr. Popkin said.
Nowadays, more and more often, complex systems are built by assembling together different system components.
DBMSs are more and more often required to integrate with other infrastructure parts of their environment.
More and more often, the two-state solution is pronounced dead.
Long before inundation occurs, people will be hit more and more often by coastal flooding.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com