This is the point where someone says that per capita isn't the right way to look at it because the atmosphere doesn't care about our arbitrary lines on the map.
They will be correct that the atmosphere does not care about such lines, but that is why per capita is a much better measurement than per country.
Suppose the total emissions the would can handle is T and there are C countries, and so the if you go by country fair share for each country is T/C. Suppose country X is having trouble staying under that. X can address that with a split into two countries, X1 and X2, carefully constructed so that half of what X emitted comes from each. Now each country's share is T/(C+1), and the X1 and X2 together have a limit of 2T/(C+1).
The ratio of what X1 and X2 together are allowed to what X was allowed is 2C/(C+1). Current C is ~200, giving a ratio of 1.99. If X had split into X1, X2, and X3 they would each get T/(C+2), for a combined 3T/(C+2) and a ratio of 3C/(C+2) which presently is around 2.97.
Split your high emission country into several smaller countries with the high emissions distributed approximately evenly between them, tie the countries together with trade agreements and various reciprocity treaties (kind of like the EU) and with no change in actual emissions you go from being over your quota for global emissions to being under.
Of course everyone else can do this also. Every time someone does it the per country quota for everyone else goes down slightly. As high emitters environmentally gerrymander their way under quota, that will eventually cause some countries that were under quota to be over, pressuring them to also split.
In the limit, you end up with something equivalent to per capita.