Next you need some territory.

That might be the difficult part as treaties signed internationally in 1967 state that space is not any one countries territory and is the province of all mankind.

This does imply that a space station can't be sovereign territory as the space it's in belongs to everyone.

Therefore you can't have a space nation, just a group of earth nations teaming up to build a station for the benefit of all.

That is unless said treaties are abolished first...

I assume this is one of the two reasons (the other one being able to deport/expel individuals) why they only accept people with dual citizenships. It's a way to weasel around the law, basically rendering the "space nation" a mock -- but still effective as advertizing gag.

That being said, I think there are effective ways around the problem of space belonging to no nation. First, the "space nation" did not sign the treaty (obviously, they don't even exist yet), so it's not legally binding for them. Sure, if they want any kind of cooperation from the other nations, they wprobably will have to.
On the other hand, there's probably ways to weasel around the laws. Do you really think that e.g. the USA will gladly accept that you board one of their espionage sattelites because "the space they occupy belong to everybody, thus they belong to everybody"? Do you think Russia or China will?

Also, property law is full of grey zones and contradictions. The ground that I own on this planet belongs to Germany. Wait, what? I mean, I own it, right? Right, but their law still applies whether I like it or not, and I cannot call out my proper nation (otherwise Alto Adige, Pays Basque, and Catalonia would already be proper nations... oh, and Bavaria, too).

Where does my property end? Nobody knows exactly, and it can change at any time.

Upwards, my property goes as far as I'm reasonably using it, above that is public airspace. What is "reasonable"? Nobody can tell. Whether I have a bungalow or a 250m tall windmill is a very different thing in terms of "using". If I have a skyscraper, does placing a huge antenna on top extend my property? Don't ask me, but I guess it probably does!

Downwards, again, my property extends as far as I'm using it, including anything I find in the ground. To the Earth's core, in theory. But only if I'm using it, and I'm only allowed to dig 100 meters deep, except if I fill out the forms for a mining license. In which case I can dig a 3km deep tunnel if I wish, and everything up to 3km deep then belongs to me. Funnily, without a minimg license, I'm not allowed to remove what's legally mine from the ground (even if it's only 30cm under the surface). Except water, which is, cynically, one of the most precious goods... except in regions where ground water is protected, except when you fill out some forms, except...
Funnily, this means I could legally steal my neighbour's gold or oil if there is any (which belongs to "everybody") as long as I file for a mining license on my ground and I'm mining deeper. Nobody can tell me not to mine sideways... law is soooooo fucked up.

Now I'm sure there is a similar weasel way of getting "your property" rights in outer space.