1
general::
adj. doing sth VERBS be ADV. 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. PREP. 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. having promised to marry sb VERBS be | become, get The couple got engaged last month. PREP. to She's engaged to an actor.
Oxford Collocations Dictionary