Steps to owning a Rock Hermit Asteroid could involve ever-increasing costs.
The cheapest, at 10,000 credits could be "Sponsor this Rock Hermit Asteroid"...and many such asteroids are already sponsored by someone else so you can't sponsor them.
Doing that would make that asteroid always appear in the same system, although it could be at a different spot for each system visit and also have small numbers (0-4) of regular asteroids around it to mine. Presumably, it has very weak transit engines capable of moving it 1 km a day? Or it gets pushed around by a "tug" ship. (Basically making it appear like an added-on-demand Pirate Cove...minus the part about being hostile.)
Whether this should also give tiny amounts of credits per day awarded to you on visiting, I don't know...perhaps as an upgraded form of sponsorship?
Once you've already sponsored an asteroid...you'll want to upgrade its facilities! Such as:
Giving it better shields (shield boosters/military shields/more energy/higher energy regen rate) -- will require a different ship for each one.
Acting as a storage depot for your cargo. (up to 1000 TC?) This would require some clever scripting, like what Hypercargo does...with the difference that this works only when docked with this asteroid and doesn't fail. Maybe even have orders to shuttle this cargo to the main station little-by-little to sell it off when the prices are high?
To make this more of a mission OXP, many of the upgrades may require specific cargo loads, credits, and significant time to build. The credits covers the arrival of work crews via shuttles/freighters as well as the equipment costs they need. You might even need to defend the supply line to the main station, especially if word gets out to big pirate gangs or other rivals...
(similar to what Oo-Haul does.)
Improving docking facilities and commodities market so some/more trader ships visits the asteroid. (Basically converts it into a Free Trade Zone.)
Improving (hired? bought?) shuttle traffic from asteroid to main station to transfer ores/cargo. (Adding shuttle traffic via scripts isn't too hard.)
Add a beacon buoy (or building such into the asteroid itself) to increase the number of trader ships visiting...at the expense of also attracting possible trouble? (Somewhat duplicating Rock Hermit Locator, except people won't have to pay for that extra to find this place.)
Increasing the number of defense ships hired to defend the place. Either requires a new asteroid ship with the extra number of defense ships, or can be done through mission scripting.
Buying/improving the quality of the defense ships hired to defend the place. (Vaguely like how Hired Guns OXP works.)
Equipment buying/selling at the asteroid could slowly become higher tech level as the asteroid is upgraded, though probably around TL10-12 should be peak and cost a gold mint.
Equipment prices could also become cheaper once you pump a LOT of credits into the asteroid for various upgrades.
Getting your ship overhauled here could be given a discount, though if this place is lower TL than nearby systems you're better off going to them instead.
At some point, the asteroid gains its own shipyard buy/sell menu...though you still cannot "park" your ship here as a garage and get it back later because of game limitations.
Mounted equipment on your ship might be removable/re-addable with some clever scripting though! This should cost some credits...maybe 10-100 credits? (cheaper if you've upgraded the asteroid more.)
Not that I've ever seen it, but what's stopping a station from having missiles as defensive weapons?
If that's possible, a somewhat upgraded asteroid might have a small launcher with a small number of missiles...and the most upgraded asteroid would have a maxed-out battery of hardhead missiles. I think it could have 32 such missiles without doing any missile-adding scripting tricks.
By the time all the upgrades are completed, (and they should take TIME to do as well as credits) your asteroid could resemble the Seedy Space Bars found in Random Hits -- because all the extra add-ons could not possibly fit inside a standard Rock Hermit's diameter.
Having said this, you should probably only be able to own 1 asteroid...at least per Galaxy Chart?
The reason for this is partially because of the likely savegame size increase caused by having to save all the asteroids with their various states of upgrades, as well as game balance issues.
I guess you could change asteroids by UN-sponsoring your current asteroid. This could cost ~1000 credits, to discourage doing it lightly. Whether this causes the asteroid to "disappear" when you revisit the same system will be left up to whoever dares try code such an OXP!
It will be like your home base, and "save anywhere" like feature should definitely work here. Make sure to choose it in a system you like!