Do I want backlinks from companies my site has a business relationship with

[McTaggart]

I automatically think yes... but nofollow links will be safer - that would be my choice as I always err on the side of caution... If I reached out to the entire network with quality content, as I would through a PR campaign, I am wondering whether the pre-existing business relationship would mean the link wouldn't be seen as truly independent by Google.

Your thoughts would be welcome, Luke

[GastonRiera]

Hi Luke,

Yes you do want those links.
I'd rather them being dofollow and only in a single page, such as blog post.

Remember to be cautious enough not no be obvious to google. For example, do not make links reciprocal (they give you a link as you give them a link). 
And of course these links should not be your only links, i believe that you already know that.

Best luck.
GR.