Stealing systems is a pretty bad idea in my opinion.
I think instead what they should have is a special class of ships named "Mining Vessels" which they can place over any unclaimed celestial body and which extracts resources from it. This ship would have a Mining Policy, similar to Bombardment Policy, with heavier settings getting you more stuff faster, but causing ecological damage to the body, applying temporary modifiers. These modifiers can lower habitability on planets, or temporarily or even permanently removing Mineral/Energy/Science Deposits. These are what would cause issues.
If the Nomads are at war with a country, then they can destroy their mines (possibly getting a lump-sum of minerals for doing so to represent that they live off salvage) and move their Mining Ships into place, encouraging a Raiding Strategy that targets Empires that are in some way distracted. Since Nomads cannot take a planet, their permanent damage is limited, so Empires in a major war that they would risk losing territory in would be inclined to ignore them.
Pops would live on Mobile Habitats, that's fine, which could produce Energy and Science, but not Minerals. This allows more diplomatic Nomads to instead trade their Surplus Energy for Minerals, since currently the only thing Positive Energy is really used on is for Terraforming and clearing Blocks, things that Nomads obviously don't care about. The Nomads could still have Science Vessels, with these Vessels, when Surveying a ship, possibly extracting some Science from it, again adding a temporary or perhaps permanent modifier or removing the Science Deposit. Again this would be a Policy like with Mining, allowing Nomads to be nice.
This could then also serve as the foundation of a possible Piracy System. Pirates would, however, instead of having Mining Ships and Mobile Habitats, would establish Primitive Orbital Habitats, like the one created by the "Birth of Piracy" event.
You could then also have a diplomatic agreement which allowed Nomads to mine inside a Nation's Borders, possibly with some payment like an Implied Tributary Arrangement. So they get to mine, but pay 25% of the Minerals they extract. With this, they could even mine areas which already have Mining Stations, allowing an Empire with a good relation with Nomads to actually get more from their mines than is otherwise possible. If you pacify and establish mines in the Crystal Hive System, Nomads would really start being interested in you.
Which could THEN serve as the foundation for a system to handle Private Industry and Mega-Corporations because such agreements would allow them to build Mines in the land of their home country, thus mean they wouldn't need to necessarily project their own borders, because that causes problems in my experience.