If you want to know more you should familiarise yourself with the work of Elinor Ostrom.
The only solution that I can see would be for those who own the commons to pay the profit that they gain from that ownership to those who do not own the commons. Which I guess is effectively Georgism.
Take, for example, the problem of limiting CO2 output. This is a global problem; there is no way to realistically privatize it. but, at least the people under the same treaty could tax the common forms of CO2 output.
Charging per ton of CO2 output, many economists believe, is better than simply regulating how much CO2 a person can output because by giving it a dollar per tonne value, you are encouraging the market to eliminate CO2 output where it's cheapest and easiest to do so, while allowing the market to continue to output CO2 where it would be really expensive to avoid.
'cap and trade' is a variation on this that is similar but different; instead of setting the economic price of a tonne of carbon, for example, you set an absolute limit for how much carbon can be released, and then lets the market decide what to use that for.
Then, as many countries have discovered, you have another problem...
Interestingly, you hint at, but don’t really acknowledge one of the classic solutions (typically pushed by the libertarians): privatize the commons. This is equivalent to your intuition of trying to set N=1.
Of course, the other classic solution is regulation, which is not too far from your union example.
Of course, both the classic solutions have downsides. Privatization makes it harder for everyone to share the good, and also leads over time to stratification and unequal society. Regulation means bureaucracy, which easily becomes captive to politics and money.