“while involving” is a correct and usable phrase in written English.
It is typically used in the middle of a sentence as a way to connect two ideas, clauses, or phrases. For example: The project was difficult, while involving a great deal of organization.
The line managers did deal with Blondie, but it took a while -- a long while, involving a heated argument, a storming-off-to-talk-on-the-cell-phone and a near-altercation before Sour would step out of line.
For the bosses, the plan was to use the entire screen while involving as few moving sprites as possible "to fool the player into thinking the whole thing was alive".
A question is an excellent way to do this while involving the other person and clarifying anything you're unclear on.
While involving itself in the minutiae of laboratory operations, the department never seems accountable for anything.
Then come the California years, when he captures the light of Los Angeles in paint and photography while involving himself in projects from opera design to fax art.
Filming on Super-8 and transferring to video, while involving expensive post-production, meant Jarman could shoot without having to rely on the conventional film industry.
The deal, which has been suggested for a while, involves Premier paying 70p a share for Encore, pushing its target up 27.25p to 72.5p.
So it makes sense that the first exchange the cousins had in quite a while involved green.
"All he did was carry himself like a congressman" while involved in the ventures, Mr. Trout said.
But even while involved in the television business, his enthusiasms took him in different directions.
(He also had Body Movin' playing while involved in a Caitian ménage-a-trois in Star Trek Into Darkness).
