I think Acraven has pretty much nailed it. I don't know Italy well enough to use that as an example: Imagine making a city like Berlin your home base and staying there for your 90 Schengen days. Now within that time you could explore Berlin at your leisure, and you could make wonderful day trips into all the neighboring towns, Dresden, Erfurt, Leipzig etc., and to some beautiful natural regions within a radius of, say, 200 km. I am sure that this can be a great way to spend three months, and I am sure you wouldn't be bored a minute.
Having said that, there are some major drawbacks to this solution: You can hardly experience any of those day trip destinations in the evening, like enjoy a relaxed dinner or a concert, unless you spend money on an extra hotel night. You have a very limited radius of what you can visit. Of course you can get on a train and go three hours one way and back in the evening - we've done that kind of thing - , but that will leave you with about five hours in place. That might be worth it for some very specific interest destination, but not normally. And you definitely cannot take day trips that make any sense to places like Munich, Prague, Heidelberg, much less Amsterdam or Paris, no matter which means of transportation you use.
So, unless I totally misunderstood your idea of a "home base", why don't you consider making that several home bases depending on your main interests, and depending on the pace you might want to move on.
Giving yourselves two weeks in one place for instance would seem like a very comfortable pace to me, and you could explore the Schengen part of Europe in a relaxed way and in depth from six different home bases.