Collocations for engaged - adj.

be

deeply, heavily
those who are deeply engaged in party politics

fully, totally | largely, mainly, primarily | directly | constantly | currently | actively, busily | otherwise
I''m afraid Mr Wilson cannot see you now as he is otherwise engaged.

in
She was engaged in conversation with a client.

on
He is actively engaged on several projects.

with
Mrs Scott is engaged with a customer at the moment.

be | become, get
The couple got engaged last month.

to
She''s engaged to an actor.