"being done with" is correct and can be used in written English.
It is typically used to refer to having completed a task or activity. For example, "I'm so relieved to be done with my final exams!".
It's all being done with the wrong mindset.
"They look forward to justice being done with this case".
The bonus is that it's being done with such verve.
Jaeger added: "What is being done with all this money?
This work is being done with Pat Hanrahan, Greg Humphreys, and Matthew Eldridge.
This is a different experiment that is being done with the containers.
And you have to look at the business and what's being done with the money.
Where does our nuclear waste come from, and what is being done with it?
This poses an important question: what is being done with our sensitive, private location information?
But there is concern that too little is being done with counselling in general.
That this is being done with Toyota's sponsorship seems paradoxical, but life is complex.
