Although there is a great deal of variance on how civilizations choose to conquer and expand, some rules can be applied universally.
In the context of world history, it is important to view imperial conquest as an investment. Powerful individuals within a culture (i.e. military leaders, nobles, kings, etc.) invest money in the development of a military infrastructure capable of fielding armies for conquest. Once the soldiers are recruited, equipment distributed, and the logistical structures necessary to supply the army are in place, the military force can be mobilized and sent into a target region.
Failure of the army to conquer a target means that the investment didn’t pay off, and those “investors” may or may not decide to try again. If the military excursion is successful, however, the leaders of the army may incorporate conquered provinces in an attempt to continuously extract material goods which will both pay off their initial costs and hopefully earn additional profit. The profits earned from the initial conquests can be used to fund additional military excursions which will hopefully reap more profit. This is the basic cross-cultural idea behind imperial expansion.
This is where the theory of diminishing returns begins to take effect. As an empire expands and gains more and more “capital” (i.e. money, resources, etc.), the sociopolitical complexity of that polity will naturally become more complex. For example, the Aztec conquests throughout Central Mexico resulted in the massive accumulation of material goods throughout the Valley of Mexico, especially in Tenochtitlan. This led to a population explosion, with the Valley of Mexico’s population increasing three to five fold over the course of 200 years.
The increased population required more resources in order to sustain, especially as the elite began to expand their influence throughout the empire. Even if conquest is halted, complexity will continue to increase so long as material goods are brought to the imperial center. Based on this model, continuous conquest is needed in order to sustain the empire.
The ability of an empire to continuously conquer territory is reliant upon a variety of factors. As a universal rule, however, target regions which are far away from the imperial center are far more expensive to conquer than regions which are closer. In order to conquer regions outside of the immediate periphery, expensive logistical structures with the ability to support long distance campaigns for extended periods of time are necessary.
Eventually, as an empire begins running out of territory to conquer, long distance campaigns become far too expensive and conquest no longer generates enough profit. This is known as the point of “diminishing returns”, when the investment no longer makes profit, but breaks even instead. When the investment reaches the point of maximum yield, the expenses exceed the profits and sustainability becomes impossible.
This is how many empires begin to go into decline. When imperial polities reach their maximum potential territory, the cost of sociopolitical complexity will continue to increase, and gradually cause the decline of the entire civilization.
However, this was not the case with the Aztec Empire when the Spanish arrived. The empire was at the height of its power and continued to expand in all directions, indicating that it had apparently not yet reached its maximum potential territory. How much larger might the empire have been if the Spanish hadn’t arrived? Frankly I have no idea. Its practically impossible to estimate something of that complexity, especially when it occurred nearly five centuries ago.