Looking on the internet deeply has found these results:

to follow up with is the most popular phrase on the web.

to follow up on 130,000,000 results on the web	to follow up with 133,700,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
I just wanted to follow up on our conversation about... We need to follow up on this Ramirez victory with something really special. I'll tell them Langley sent me to follow up on the kidnapping. You asked me to follow up on the information. You have to follow up on hilton head. I thought we were here to follow up on Gemma. You sent Ziva to Israel to follow up on a lead. National Parliaments are urged to follow up on EU 2020.	But then I am almost convinced that we have to follow up with quantitative restrictions. Now you have to follow up with something romantic. Please don't forget to follow up with Niko. Arguing over who was supposed to follow up with levI's parents, still thinking every mistake could be avoided. Jake volunteered to follow up with the M.E. He came in early to follow up with the phone company. I need someone to follow up with the girlfriend in the Hopkins case. Now he wants to follow up with me this afternoon.

to follow up on

130,000,000 results on the web

to follow up with

133,700,000 results on the web

More popular!

But then I am almost convinced that we have to follow up with quantitative restrictions.
Now you have to follow up with something romantic.
Please don't forget to follow up with Niko.
Arguing over who was supposed to follow up with levI's parents, still thinking every mistake could be avoided.
Jake volunteered to follow up with the M.E.
He came in early to follow up with the phone company.
I need someone to follow up with the girlfriend in the Hopkins case.
Now he wants to follow up with me this afternoon.