The phrase "already overpopulated" is correct and usable in written English.
It can be used when discussing a situation where a population has exceeded the capacity of a particular area or environment.
Example: "The city is already overpopulated, leading to increased traffic congestion and housing shortages."
Alternatives: "already overcrowded" or "already saturated".
Europe is already overpopulated.
Of course, you might argue the world is already overpopulated.
By the way, a significant drop of environmental impact of products cannot be achieved by simply adding a „green‟ constraint to the already overpopulated list of design constraints.
Dark greens say the world is already overpopulated; bright greens suggest that with more efficient farming, we could feed another few billion.
Considering that it's an already overpopulated continent, it's surprising that many European countries give incentives to families to make more babies.
My own parents, zero-population-believing hippies, told me that they adopted me because "We had two biological children and we wanted another child, but didn't want to bring another person into an already overpopulated world".
Internationally, I wonder if population-increasing technologies (eradication of diseases, chemical controls for malaria, etc). in already-overpopulated areas condemn future generations of humans and other species to ever-lower standards of living on an Earth with finite resources.
There are those who look at scenes from Calais, Lesvos and the Hungarian border, and rather than feel the overwhelming rush of empathy that accompanies the horror, explain that, actually, this tiny island is so overpopulated already we're struggling daily to stop our children being nudged off cliffs and into the Channel.
It's also one of the most populated areas of an already hugely overpopulated country.
Everywhere to which an alien might wish to take refuge is now overpopulated, and already with problems of its own".
The pond is overpopulated.
