chase around after (someone or something)
To seek someone or something in a variety of places. I chased around after Bill all day but never found him—apparently, he was out sick. I went to five different hardware stores, chasing around after that part for the heater, but I still wasn't able to find it.
chase around after someone or something
to look here and there for something; to seek someone or something in many different places. I don't want to have to spend a whole day chasing around after exotic ingredients for this recipe of yours. I chased around after Roger and never found him.