The peak populations on Earth could be more than people think. IF this was done to merely maximize population then the Earth could possibly be maximized to many thousand (or even more) times our current population.
First: The Space and Utilities. --Humans have been building skyscrapers for centuries so for space we can just go up once we have used all the space on land. This will allow also for easier energy capture via solar panels for example. There would be no need for travel so making the earth basically one large skyscraper could allow it to tower thousands of feet. We can also utilize the ocean space as well. With the ocean being 95% unknown there is probably a mass amount of space to be utilized. If we lowered sea level by extracting sea water from the oceans and then recycled the water that could not only create more space but also increase resources. This extra space where the sea once was could be used to create nuclear energy which has the one of the highest energy/waste ratios.
Second: Population Needs. --Although different people consume different amounts of food/water this can be standardized. There are 2 ways. One is genetic modification. 279
Using gene modification scientists could make people smaller/shorter which would not only increase the space available but also the food/water needed. Genetics could also be used to allow parents to have maximum offspring using an artificial womb nursing thousands of children at once. Second is hormone modification. Even if the population was not genetically standardized it could be stopped growing by stoping growth hormone in a person before they get passed the minimum required to live and reproduce. These smaller people will consume less allowing for less space for growing food would be need per person.
Third: Food Selection. --Water could be obtained from the extracted ocean water which would supply generations of populations and don't forget the ice caps. GMOs (genetically modified organisms) could also be used to make food denser with certain nutrients and to allow them to produce the nutrients necessary only. These GMO's would take up much less space and could even be modified for reasons other than food.
Forth: Oxygen Dependance. --Oxygen will be need by this smaller population still even though it will need less per person. Oxygen could be extracted from the ice caps which have oxygen trapped inside and even the ocean water if worst comes worst. With this population being housed in this "Earth Skyscraper" the roof could be utilized for plant GMO's that could produced the max oxygen per area and be nourished using the population wastes (CO2, fecal matter, etc). This symbiotic relationship can maximize the capacity of Earth's population. 335