"follow up on" is a correct and usable phrasal verb in written English. You use it when you want to discuss taking further action after taking part in an activity or events that has already been completed. For example: "We should follow up on the results of the meeting to make sure we meet our deadline."
Follow up on invitations.
Then follow up on your threat.
Must follow up on this.
Anyone want to follow up on that?
"We will definitely follow up on this".
MR. LEHRER: We'll follow up on this.
Failure to follow-up on customer receivables delays.
You need to follow-up on him.
I'm left handed!" Follow-up on this.
A follow-up on the first story.
Clinical follow-up on a quarterly basis.
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Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia