This is simply an opinion, based upon observations and interpretation. I don't know for sure how google views this. I don't think that anyone outside of Google knows the real answer. If anyone has their own opinion, I would like to hear it.
If you go to Amazon.com (not the Amazon.com Business site), you will see that they have site-wide links to dozens of their other retail and service properties in the footer. These go to Zappos, Diapers.com, Casa.com, Goodreads, Woot and lots more. In my opinion, I believe that these are simply viewed by google as Amazon parent company linking out to their other properties. If you go to these other properties you will note that none of them have this huge collection of links in the footer. I see other large companies linking out to their other properties in a similar way. But these are always going from the parent company out to their smaller web properties.
On the other hand, Hayneedle (a large muti-site retailer who runs over 200 retail domains) had severe ranking problems a couple years ago. This problem occurred when most of their retail sites had a huge navigation on many of their websites that contained links from lots of their retail sites to lots of their other retails sites. Hayneedle's rankings recovered somewhat a short time later, when these huge interlinking navigations were removed from their websites. In my opinion, this was viewed by Google as a manipulative linking scheme because you had sitewide links on lots of domains, each directed to lots of other domains. This was a huge number of links totaling in the millions.
In my own practice, I own multiple sites, but I don't place site-wide footer links on any of them because I think that it looks irrelevant and dumb. I also do not believe that it would have much ranking benefit at all. I believe that Google knows who owns the sites, and I believe that they have enough information to dampen your ability to promote your own sites to higher rankings with a heavy amount of "manufactured links". (All of my sites are connected to my personal google account through webmaster tools, so Google knows who owns all of them. They all also have my adsense codes on them and display ads on every page.)
I don't have fear or hesitate to link from one of my properties to another of my properties if I have relevant content there that exceeds what is available on the linking page. Does that have ranking benefit? Maybe a little. But I don't believe that site-wides between your sites are a good idea because there is a lack of relevance. And I don't believe that your visitors are going to investigate a dropdown menu in the footer to see where it goes. So, I don't think that there is any reason to do it.