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Perhaps a more useful rule of thumb than "I have tank addiction, join us" would be to have the tanks you need to dive as you want. That could be a large number or it could be a small one. Many recreational divers are served by a simple pair of al80's. In Great Lakes recreational wreck diving, it is hard to be beat a pair of hp100's and an al30 or Al40 as a pony. Folks who don't want to visit the dive shop for fills after every charter often choose to double or triple their primary tank inventory for reasons of convenience, or if they are providing tanks for other divers.
That covers the basics. The next level in building you tank garden into a tank farm is configurations and gases. Twinsets require a pair of tanks that are dedicated to being in a twinset, and as soon as you get into trimix you are realistically going to need multiple twinsets. And multiple deco tanks and stages. Want to do sidemount? More tanks. CCR? More tanks. You get the idea. And it's not just any old tank, of course. You'll want tanks that fit the gas plan and buoyancy characteristics for the diving you're doing.
As a new diver, I suggest not worrying about the second phase unless and until you're ready to get into such diving. It will take years of building training and experience anyways before you need the stuff to go do such dives. Collect what you want to do the diving you want to do. And always buy in pairs if possible.
I'm sure they gave you some steel 72s. Make a small set of doubles from them: independent, isolated maniford, whatever. Of course, then you will want two of those to not change gear for that day, so that takes care of 4 steel 72s and gives you long dives and redundancy underwater.
(Or LP50s or AL40s which make really nice tiny doubles, but people are less likely to be clearing those out of their garage.)
If anyone is clearing out matching lp50's, let me know those make great shore diving doubles
It is my opinion that once you go beyond around 4 tanks that you really need to be able to VIP your own tanks or it is going to kill you in shop fees