Advice on Displacing Bad Results

Hi all,

Situation:

I have client with some aged negative articles showing for their name in search results (across multiple keywords).

There also are quite a few positive articles within the same set of results.

I would like to push these positives up and over the negatives (displace them down results).

All sites for both positive and negative are high authority sites.

Question:

What backlink and anchor text strategy would work best to get positive movement here?

Would be interested to hear method suggestions on this (ie: GSA? PBN?, link-volumes, anchor-text profile em,pm etc).

Many Thanks!