Multiple websites linking to one blog

I have multiple websites that target different city keywords for my company and I was wondering if it might be better to have one juiced up blog that links back to all the websites vs each website having individual blogs? I have a competitor that does this and they rank number one in each city they are located in for the most money keyword in our niche. They have a "blog" on each website but once you click the blog post (they are the same on each website, posted the same day) it goes to just one blog website they have set up which links back to each city website they have set up.

I'm thinking of doing this for my website. Thoughts?

Not sure I follow what you're asking exactly.

I think it's important to have regular activity on all sites, including your PBN's. So something like a blog that is getting fed content each day is good on everything. You can do more with 1 website by adding in more categories and getting content pumped in from relevant RSS feeds for each category. Automate this over time and you'll see the sites getting more natural traffic and natural links that power everything up. Then you can go back in and find the indexed posts and link those back to your money sites that you're trying to rank.

it's just some kind of PBN with keywords targetted,
the fact that these websites do rank make them even better, especially if they do hold some decent links,
you might want to consider hiding the footprints in such a case as well