I don't know if it was my timeline being referenced with mention of an Etruscan Empire but I feel it's relevant here. The Etruscan 'Empire' of my timeline is about the most extreme I feel the Etruscans can go with a POD as late as 480 BCE, and that extremity is basically modern Italy+much of the surrounding Alpine regions. That's it. Oh and Corsica. The Empire in question is only an impressive structure because there is nothing like the Roman Empire ITTL to compare it to. Indeed, that expanded state is from the last 20 years' of that ATL state's lifetime, and it's a direct factor in its total collapse. I feel like I pretty much explored the extremes the Etruscans *could* have gone to in that period without something ridiculous like giving them an Etruscan Alexander. The house the ATL Etruscans built was small, but the kind that you never forget after you've seen it.
The Etruscan League certainly could have centralised, either OTL or in your proposed situation of conquering a large chunk of Italia, there were temporary heads of the League with the power to command their combined armies in the field, it's a solid institutional platform. Their history demonstrates the capacity for political and state development, they certainly had the imagination to change the way their political affairs were conducted; for example, the office of zilath morphing from hereditary kingship to a magistracy, or even the shift to the institutionalised city-states in the first place. The problem is that they only regularly started to combine forces like that once they realised that the Romans had morphed from errant-colony to a serious menace to their independence, at which point this is already becoming a matter of 'the Etruscans don't lose to the Romans, either short or long term, the same way as the real 4th-3rd century BCE' which is a somewhat tall order. If they've reached the state of dominating Italy you imagined, I would say they already would have to have achieved a degree of workable unity, or had come under the thumb of one of the other cities, probably Tarchuna/Tarquinia based on its relative size and power.
The three biggest, or at least most predictable, OTL menaces to the Etruscans after the 5th century BCE (effectively their political apogee) are Celtic speakers in the North, Romans to the direct South, and the Greeks further South. None of these are easy things to deal with; the Greeks in Italy were no slouches, Syrakuse especially; the Celtic speakers to the North have many reasons to move south, the wealth of the Po valley being only the most obvious; lastly, archaeology indicates that 6th century Rome was already one of the largest cities on Italy, any Rome that survives Brennos' horde would be in one position or another to become a major Italian power. An Etruscan state or political sphere that lasts for a lot longer is possibly going to have to deal with either Germanic speakers or the population pump of Europe they helped contribute to.
Timelines where the Etruscans are given the room to develop new political structures, and centralise, probably need at least one of those 3 OTL forces to be hampered in some way. I've seen a few timelines where Rome is interfered with early on, for example being destroyed in 396- that doesn't remove the influence of Celtic speakers pressuring the Po Valley but it was the Romans that proved the existential threat to the Etruscans in the end. On the other hand, removing the invasion of 396 benefits Rome but removes the Etruscan loss of the Po Valley too, at least at that date, which is part of why the Etruscans were more vulnerable to the Romans in the early 4th century BCE. Likewise, the invasion had a pretty big impact on Rome's own cultural development and political ambitions, so there's all of that to be reckoned with too. My timeline, by contrast, has the Greeks be interfered with. This is more unpredictable but you could be talking about wider Etruscan domination over Campania, if the coalition that defended Cumae OTL can't come to the rescue for some reason (Syracuse losing Himera?). for example, and the Greeks in Italia slowly becoming something similar to Ionia under Lydia, followed by the Persians.
There's a lot of open possibilities for the Etruscans, even as alt historians we can sometimes go down the same predictable rabbit holes. With Rome conquered by the Etruscans, would you get tension with the Carthaginians? Not at first, no, there's a fair amount of evidence Carthage and the Etruscans had a very privileged trade relationship. But sooner or later the situation is going to change; the status quo already altered to have the Etruscans occupy and nom upon Latium, it will doubtless change again, either with the Etruscans having new ambitions or pressures or the same with regard to the Carthaginians. If they came to somehow occupy all of Sicily, say, sooner or later they are going to have a new problem, or find that owning certain parts of Italy are advantageous, or get brought onto the mainland via wars with the Italiotes. After all, the Carthaginians and Romans were frenemies in a fairly stable relationship for a long time, but their needs and changing situations changed the nature of the relationship. If you have a big paradigm shift occur to cause an ATL or as a result of the POD, sooner or later there's going to be others.
