De-Ranking a government local PDF?

I have someone needing help with a pdf doc on a gov website that is coming up in local when his name is searched for. It's not a .gov domain however. If I search for his name in another state, the PDF doesnt come up.

He has a lot of social media profiles surrounding this pdf.

I've never been asked about something quite like this. Wondered if anyone had any suggestions.

You can't delete it, but you can push it down in the rankings by getting lots of PDFs matching his name to outrank it.

You can also control the message then...

The Official PDF for John Doe: unrelated to the Internet Troll PDF ...

Does it have to be a PDF that out ranks it? Or is that just the easiest, fastest way?
Are their PDF depositories or something I would use, then just throw backlinks at it?

doesn't have to be... wasn't sure if the audience was expecting a PDF in the search or not. Has to be a lot of different domains to pull it off... you are basically talking about taking over a page of search results which is very very hard to do. If normal SEO is 1x difficulty then this is 10x difficulty at least.