The term 'deeply involved' can be described by the crossword solutions RAPT (4 letters), UPTOONESEARS (12 letters) and UPTOTHEELBOWSIN (15 letters). RAPT means to be completely absorbed in something, UPTOONESEARS means to be involved to a great extent and UPTOTHEELBOWSIN means to be deeply engaged. All three solutions indicate that someone is very invested in something, whether it be an activity, project or relationship.