ADJ with n
The 'involved' group
These adjectives indicate that someone is busy with an activity, or has a close connection with an activity.
The former first lady is busy with charity work and other projects.
She has been involved with athletics since she was eight.
Liz was quite happy to work on the garden while Chris was tied up with his new business.
In the case of busy, involved, occupied, preoccupied, and tied up, the preposition with is sometimes followed by an '-ing' clause.
busy embroiled enmeshed entangled entwined involved occupied preoccupied tied up
Most people are preoccupied with scraping together an existence.