While I would highly recommend not upgrading a production environment to a .0 release, if you're going to do it the main concerns are
you want to follow the tiered approach (master, search, peers)
You don't want peers online with different versions as major releases will introduce different communication methods.
So for you, you want to follow the standard cluster upgrade procedure: master, search, master in maintenance mode, then when you get to indexing layer, because multi-site, you want them all off before starting as you're doing a major release. It seems like 7.1 will introduce a better upgrade procedure so maybe this would be your last time doing it exactly this way.
The docs indicate when upgrading a multi-site cluster you can go site-by-site but ONLY if you're doing a minor version. Confusing cause they don't list your exact plan to go from 6.6 to 7.1. If I were you, I'd take down all the indexers at all sites, upgrade one site, start it, then move to the next site (again, this is all part of step 3 in the tier'd approach listed).
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