The phrase "are engaged on" is correct and usable in written English.
It can be used to indicate that someone is actively involved in a task or project.
Example: "The team members are engaged on the new marketing strategy to boost sales."
Alternatives: "are working on" or "are involved in".
Now, virtually all of the Yemeni troops that had worked with the U.S. are engaged on one side or another of a three-pronged political struggle between the remnants of the Hadi government, supporters of former President Ali Abdullah Saleh, and the Houthi faction, U.S. officials say.
Some members of the Secretariat are engaged on permanent contracts, but others serve on temporary assignment from their national governments.
Anna and Claire (Zoë Wanamaker and Anna Chancellor) are engaged on such a relationship; their maid (Lyndsey Marshal) is a lusty little hetero.
You are engaged on a double task, recovery and reform - recovery from the slump and the passage of those business and social reforms which are long overdue.
"Frequently, workers are engaged on projects for less than three months, meaning companies are not obliged to offer the worker the opportunity to sign up for auto enrolment.
The President is seriously handicapped by the fact that 60,000 of his best troops are engaged on the Mongolian frontier in checking the advance toward China of the Hunghutzes, the band of brigands which is now devastating inner Mongolia.
"In Qusayr, the ones who are engaging on the front lines, the man-to-man firepower, that's Hezbollah," Mr. Rizk said.
Both scammers and legitimate users are engaging on Twitter more, as in tweeting and gaining followers.
"As we move into 2015, we are engaging on community to add some zeros to these numbers".
Indeed, the cities that are engaging on the new transition in ICT are getting smarter in how to become more sustainable (e.g. [1 8]).
"We were engaged on April Fool's Day and broke the engagement on Halloween.
