hooks at dape start and exit

I've had a problem recently with at least one mode clashing with dape for whatever reason. It would be nice to be able to turn those modes off and on when I enter /leave dape. Would this be possible? (In this instance, eldoc-mouse-mode triggers something which cancels repeat-mode _: and I'd like to disable eldoc-mouse-mode on dape start, and re-enable on dape exit).