come after someone—pursue or chase a person (in order to attack, arrest, etc.):
- I heard the clicking noise from the street getting closer. It sounded like they were coming after me.
go after someone—
1. = come after someone:
- Half the guards went after the escaped prisoners but they got away free.
2. (coll.) make romantic advances:
- Antonio says Luis is the only one he’d trust because Luis would never go after his girl.