Resource Strip Mining
As mentioned above there is nothing to stop you building a medium starbase over a particular resource location with multiple resource extractors, lots of cargo and docking bays and effectively generating massive amounts of that resource (luxury or strategic) from the one location.
All you need to do is find a single source of Nekros Stones, for example, and by strip mining it you can supply your entire empires need and additionally flood the market with your abundant supplies. You can do this because there is no restriction on over-exploiting a resource location and the resources themselves are assumed to be infinite.
In a previous suggestion some posts above on this page I mentioned that this is an exploit that should be gotten rid of.
Which would work.
If the game was tweaked somehow to make resources have greater impact and meaning (eg. so you don't end up knee deep in every strategic resource once your empire achieves critical mass) then the mining of resources takes on greater importance.
So I've had a few thoughts on how to deal with the exploit beyond just unilaterally enforcing a rule that any miner can only have a single resource extractor of any particular type.
If, instead, you (eg. CodeForce) continue to allow the player to put as many resource extractor modules on top of a location as he wants. Go crazy and strip mine Lead till the lights go out.
A couple of ideas how to turn this into a positive instead of an exploit.
Making resources finite would work. The games already has the data inbuilt for this. Didn't come to pass because, as I understand it, the AI had difficulties. Make it for players only. Make it an option so those that dislike this kind of thing don't have to deal with it.
A second approach would be to have resources that never run out but that degrade in quality. For example a resource of Caslon is rated at 92%, excellent fuel source here. If you put multiple extractors over it to suck up as much as you could as fast as you could then you run the risk that the quality of the Caslon source could degrade below the 92% level to represent the fact that it is depleting.
Rough thoughts would be that once a month, for example, the game checks every mining station and if any have multiple extractors then there is a die roll that may result in random% drop in the resource quality. The more extractors you have sucking it dry the greater the odds it will drop.
Trick is that it will keep dropping until it gets to 1%. After that no more drops. Your mining station is still eking out dribs and drabs but that's about it. You have - like a greedy oil baron - taken out too much too soon and suffered the inevitable consequence.
Opens up some interesting decision points for the player. Yep, I have an urgent need for Helium. Running short of the stuff. Do I park a gas mining station on top with a standard single extractor and go for a long term reliable source while gambling that I can find more or do I go for broke and pull out as much as I can with multiple gas extraction modules installed in the miner while accepting that I might kill the golden goose?
It would also make resource quality have more impact. There isn't a lot of point in strip mining a 13% Lead deposit. You'd be hitting empty in no time. But a 90% Lead deposit might last long enough ('cause the chance of the deposit degrading is randomised) to make it worth your while.
Looking forward to the expansion.
I think you are overlooking a fairly simple and effect solution to your issue. The problem here is not that resources are finite v. infinite, but simply how much can be refined by a given star base. From my point of view, the solution would be a simple as giving a mining star base a natural extraction limit based on the extractor type used. This is sort of what they did for the medical and recreation modules, so that you can't just put a bunch on one base and get a huge bonus. If they set the limit to something around the extraction capacity of 4 extractors, then you would not be able to "overload" your extraction capacity. Yet, maybe this kind of limitation does allow the player to have that strip mining feel that one would expect. Another simple solution would be to simply limit a players total resource extractors, based on total population. This way, an empire could strip mine a few planets for an abundance of resources at the cost of slow mining a lot of different planets.