He won't be able to attend because he's 'otherwise engaged'. [=he is busy doing something else]
('US') He is 'engaged' in research. = ('Brit') He is 'engaged' on research.
She 'engaged' him 'in' conversation. [=she started a conversation with him]
(..) I'd like to better understand what motivates you. Who are you anyway? I'm an alienist. How does it feel when you're engaged in the act itself? Have you tried to stop yourself? I thought I could. I even promised my parents, but the feeling (..)2018 TvShow: The Alienist Title: These Bloody Thoughts Season: 1 Episode 4