"will proceed on" is correct and usable in written English.
You can use it when expressing an intention to continue on or continue with something. For example, "We will proceed on with our plan as scheduled."
We continue to have doubts about the possibility of negotiating an effective treaty, but are willing to move forward on the condition that it will proceed on the consensus basis traditional for multilateral arms control and nonproliferation negotiations.
Five other countries will proceed on a slower track, and Turkey will come last.
Transition will proceed on a province-by-province basis and be gradual.
The Associated Press reported Monday that elections in the state will proceed on July 4, as scheduled.
In whatever way the new administration moves, the case will proceed on a schedule set by the Court of Appeals.
Some consensus building processes will proceed on a confidential basis, depending on the content of the discussions.
I'll proceed on Baconian principles: tasting many, swallowing most, chewing a few and no doubt spitting a couple out".
Muir hasn't decided how he'll proceed on a number of key votes, including the repeals of the carbon and mining taxes.
And then following that, we'll proceed on to discuss another very important and useful mapping or design procedure referred to as the bilinear transformation.
All it did was to delete the text "(1)(A)." But I'll proceed on the assumption (just for the sake of argument) that my colleagues would at least have a leg to stand on (even if a wobbly leg) if the Senate "version" had become the law.
It also shows me that once I'm gone, life will proceed to flow on all around me, as though I had never existed; traffic stops for no man.
