If you are a company and you have several sites for different product lines, then linking between sites in a natural way is your right to do and Google recognizes this.
However, if you have several sites that are largely unrelated in that branding and product lines are not linked, then you may run into trouble. Keep in mind that branding signals play a large part in this. I count 46 branding signals, though not all of them will be present, at least half will be. Keep this in mind.
Here is a bit of what happens.
Google will look for relationships between sites including but not limited to registration information (including historical), names, addresses, phone numbers, e-mail addresses, link patterns, social media profiles, and so on. Google is very good at putting domains into realms by relationships. They will use a large number of data points in evaluating linkages/relationships between sites.
Another thing Google is very good at is looking for linking schemes between sites and will make determinations automatically and manually as to whether inter-site links are natural or un-natural.
Google hates linking schemes and if they determine that you are using a linking scheme that is devised to build rank whether it actually does or not, they will slap you silly and recovery will be long and hard. There will be nothing you can do about it either. Keep in mind that linking schemes was one of the biggest factors taken advantage of by spammers and their linking schemes were rather sophisticated- far more than the one you are proposing.
If you are creating natural links- links that any webmaster would make, then you are okay. But step beyond this, and it will simply be a matter of time and all sites will suffer a severe loss for a very long time. You would have severely downgraded your trust score with a history of spamming that is never forgotten. Trust spans all domains you may want to operate. If you have one spam site, Google is automatically wary of all sites they determine are within your realm.
You have to ask yourself this important question. Am I linking naturally? It appears that you are building a linking scheme that is not natural but intentional. I would seriously advise against this. I would, however, advise linking naturally and think marketing and not search engine influence. Think content as a product for humans and not machines.