The Macedonian dynasty of the Byzantine empire lasted from 867-1056. As one of the Byzantines more competent dynasties, were there no relatives that Theodora had at all that possibly could've succeeded her
Yeah no she was the last of her line as Basil II had no children and by time her and Zoe ascended to the throne, they were far beyond child-bearing years.
The best way to continue the Macedonian dynasty is to have Constantine VIII have a son, or the better option is to have Emperor Basil II have a son (let's say he's named Romanos III after his grandfather). Basil II having a male heir means that he leaves the Empire in the hands of a vastly more competent individual. By the time he died, the Empire was very wealthy and was arguably the strongest power in all of Christendom at that time. He also probably completes the planned reconquest of Sicily as well.
Basil also had extended his influence/hegemony in the Balkans as well, so that would likely continue in the absence of political disruption that followed Basil's death in otl.
And if the government can evolve into a constitutional Monarchy where the senate holds most of the power protecting the emperor from making lethal mistakes to the empire,
Constitutional Monarchy? The modern notion of Constitutions is anachronous to the Romans.
They already were Roman and had a Constitution through the legal framework established by Augustus and past Emperors. Rome was a Republican monarchy, and thus ruled by the will of the "Senate and people of Rome." However in practice this meant the army with the Senate being ceremonial for centuries. The nobles also were subordinate the Emperor as well.
Our modern notions of Parliament and limited monarchy stems from the Romano-Germanic Kingdoms that emerged in the post-Roman west. The King according to old Germanic traditions was elected and considered more among a "first among" equals in regards to the rest of the nobles hence why the French Kings had their own set of "peer" nobles.
A successful Rhomania and long lasting Macedonian bloodline keeps the Roman system together which was quite dynamic and would likely be stabilized now with the idea of hereditary dynastic succession gradually gaining steam.