No, you really can't analogise Mesopotamia and Mesoamerica like this. I understand and sympathise with your desire to do so, but this is entirely different turf we're fighting on. Material and cultural relations between Mesoamerican states were never "imperial" in the way you're imagining, including under the Aztecs - in fact, the suggestion that the Aztecs were any more of an imperial state on Assyrian or Roman lines than Teotihuacan was is startling to me, considering how much more we know about the Aztecs!
Due primarily to the geographical aspects I discussed, Mesoamerican society was not a pyramid but a lattice - think Ancient Greece, but on a much grander scale in terms of population and cultures - and relations between states were just that, relations. When Mesoamerican states aspired to hegemony, they aspired to dictate processes of tribute and trade that were already ongoing of their own accord. Put it another way: the state owed its existence to commerce, not the other way around. All the maps of the Aztec "Empire" that show precise, if irregular and counterintuitive, borders are fictions of the modern era, which is why they're so inconsistent. What they actually show is not even a single spectrum, but multiple spectra, of commercial relations to Tenochtitlan - ranging from the fiercely-opposed and constantly beset Tlaxcala, to minor Mexica colonies in the south, to Mixtec statelets whose interactions with the Aztecs fluctuated from trade to tribute to neglect - and every relation was exponentially complicated by unique conditions of language, military strength, agricultural productivity, and many other factors. The notion of "rule" on Old World lines simply did not exist, and the idea that the Aztecs had some kind of mystical conquering spirit that led them to impose one fails on premise. I'd even venture to say that you assume that premise simply because the Aztecs were the last indigenous hegemon of Mesoamerica. No doubt they were the most impressive, too - but they emphatically did not represent a revolutionary paradigm shift in Mesoamerican history. It's odd that you point to mass human sacrifice as a part of the Aztecs' alleged "expansionist" ideology; I'd argue the exact opposite, that it was a logical conclusion of the very lattice system I'm talking about, where the very bodies of subjugated tributaries were brought to Tenochtitlan and disposed of. Mass human sacrifice was a representation of Tenochtitlan's domination, and it doesn't make any sense if you view the Aztecs' program as one of integration.
On the other hand, the way you describe Teotihuacan is actually (Mesopotamian analogy and linear historiography aside) pretty close to the description of any Mesoamerican hegemony. It was the cultural and probably material focal point of Mexico in its heyday, just as Tenochtitlan was in its own. So OP's question isn't to be imagined as "how do we make Teotihuacan more like the Aztecs" (they already were) or "how do we make Teotihuacan a conqueror-state" (not possible in precolombian Mesoamerica IMO) but rather "how do we keep Teotihuacan at the top of the basic Mesoamerican hegemonic pattern?" That question, as I've argued already, basically demands an act of imagination; but we shouldn't confuse it for much broader and less regionally-sensitive questions, which are either misinformed or improbable.
You are interpreting too much into my words.
When I say empire, I use it in the term that the famed historian Mario Liverani used it. That has little to do with territorial expanses or controlling distinct lands, but to do with a metaphorical claim to universal hegemony of some sort. Liverani for instance, described the traditional Roman Empire post-republic as not an empire (or at lest less so than universal asserting realms such as Akkadian states, the Umayyad-Abbasid Caliphates, the Mongol Empire, the Aztec Triple-Alliance, the Papacy [1000-1414 CE], etc...) in the term of his meaning, yet certain Sumerian city states such as Uruk were entities that claimed a vast universal hegemony over the entire world, specifically by proclaiming itself as the sole-human state on the planet and so forth or other religious conceptions. Likewise, I can use it in the sense that all peoples generally, at least of certain major states, there exists a certain imperial mission, that is the reasoning for which said state exists. No regime or state argues that it exists for no reason; there is always a vast and complex patchwork of reasoning that make up an imperial mission.
Thus, the term I use, has nothing to do with the way in which you interpreted my terming. Though, for your benefit, I did not mention or specify exactly. So it is of no issue.
It is also somewhat offensive that you assume so greatly of my views... Likewise implying that I am using a sort of old-world standard. When in reality, I am attempting to add a somewhat similar occurrence in a world alien to ours to another world alien to ours. The Assyrian hegemonic presence in the Mid East, is similarly alien to my perspective or to yours. Likewise, the manner in which the Assyrian state operated especially pre-Tigalth-Pileser III is not that much different to the way in which the Triple-Alliance operated, it is not nearly as clear-cut a delineation as you presume. I am not the first persona to make these comparisons, noted experts in both fields have drawn the comparison between the two entities in their zealous hegemonic impetus that derived ultimately from a religious directive. As many have described, the Triple-Alliance existed for the sake, according to its own myths, to appease
Huītzilōpōchtli and other gods of their pantheon. This included the formation of an extremely militant martial system intended upon the acquisition of subjects (as in submissive tributaries) of all peoples within its reach and the pulling from them; resources to be offered to the gods and for the enrichment of the interior. In the case of Assyria, the goal was to 'complete Duranki;' that being, the world was given to the people of the Land of Piety (Sumero-Akkadian cultural zones) and that the Great Gods directed them to complete the act of universal conquest. In practical terms, Akkadian states, especially Assyria, operated under a motive of acquiring submissives and draining these submissives of resources and sending these back to the interior.
Thus, in the case of Assyria, I turn the same accusation toward you, that you have misunderstood Assyria and wrongfully assumed that it was not a state at least similar to the Triple Alliance. Especially in terms of its goals and reasoning for existing. There was no civilization mission, as the Romans possessed or that Imperial China imagined, but one of originally extermination of others who did not submit and then the establishment of a series of submissive tributaries who all submitted to and whose resources were extracted and pulled into Mesopotamia. If you deny that the Mexia Triple-Alliance acted this way or similarly, then I would be curious as to why you would say it is not so. To return to Assyria briefly, Samuel Noah Kramer described the Assyrian state as existing with its Akkadian like-states, as attempting to assert their region as the light atop the hill of a wasteland of the Universe, which the universe around them, existed only to serve and maintain with its lives, the Land of Piety (Assyria and Karduniash [Babylonia])
Thus, my point; I am of the opinion, that the Aztec, not due to any linear reasoning or development (as I do not believe that this is the case for Assyria either, there were periods of centuries wherein Assyrian kings became 'secular' and feigned as Divine Kings and hence lost the older impetus of Completion of Duranki,, likewise, the times wherein Akkadian realms saw to the extermination of those around them was stronger in the past), but that the Triple-Alliance reformers such as king
Itzcōhuātl ,asserted a cosmological reasoning for domination of the entirety of the known world. Which, was unique, specific and self-contained within the milieu of the Aztec experience. It was this affirmation of a certain hegemonic goal and the assertion of a cosmology, that made Assyria ultimately the most consistent realm in the Late Bronze Age and Early Iron Age, despite often having the smallest territory and the poorest selection of resources/population.
This, I argue, the Triple-Alliance possessed. It contained a clear and concise mission for its state and its hegemonic presence. It did not sustain itself only with creating blocs of influence and of asserting economic hegemony, but it furthered its power through inundating the region in an aura of terror (utilizing an Assyrian concept, whereby the notion is that Assyria continually frightens and brandishes punishments and acts of violence upon its vassals so as to constantly assert itself as the 'strong') via military action. That was constant and in-line with the reforms of early kings and affirmations of the demands of the gods, whose demand was that the people never were to become complacent. From what I understand, experts in the field of Mesoamerican history, are in agreement that the zeal of the Triple-Alliance exceeds those prior in the region.