I thought it was a fantastic book and it seems to be held in high regard on this sub here as well. Now, if I'm interested in what happened to the Roman Empire after her book ends (with the decree that every free inhabitant of the empire would become a Roman citizen)? I know at some point it splits into East and West, but it's pretty hazy from there, and I'd be interested in learning more.
Others can weigh in, but do check out our booklist!
The Constitutio Antoniniana which granted Roman citizenship to all free inhabitants of the empire was issued in 212 AD and there is quite a lot of Roman history after that. Soon follows the so called “crisis of the 3rd century” between 235 and 284 AD throughout which the empire was shaken by internal as well as external problems. Next comes Late Antiquity, a period which has attracted a lot of scholarly attention in recent decades. It saw some huge changes like Christianity’s rise to dominance or the final partition of the empire into a western and eastern half that you mentioned. And while the western part already disappeared throughout the 5th century the Eastern Roman Empire would survive for a long time further. The rise of the first Islamic caliphate in the 7th century AD cost it much of its territory and caused further transformations. This surviving remnant of the Roman Empire, now centred around Constantinople, is usually called the Byzantine Empire. Its eventful history would continue through the entire Middle Ages until 1453 AD when it was finally conquered by the Ottomans. So all in all there is more than a millennium of further Roman history to cover.
Michael Kulikowski, The Triumph of Empire. The Roman World from Hadrian to Constantine (2016) might be a good point to start as it begins right in the period you’re already familiar with and leads you through the 3rd century crisis to the beginning of Late Antiquity.
Peter Brown, The World of Late Antiquity. AD 150-750 (1989) is pretty much the foundational text for the modern scholarship on the named period. Its short, richly illustrated and just all around fantastic.
Peter Heather, The Fall of the Roman Empire. A new history of Rome and the Barbarians (2007) covers the developments that would lead to the end of the Western Roman Empire.
Peter Sarris, Empires of Faith. The Fall of Rome to the Rise of Islam. 500-700 (2011) has a larger focus than just Roman history and also concerns itself with the post Roman kingdoms in the west as well as (like the title says) the rise of Islam.
Judith Herrin, Byzantium. The surprising life of a Medieval Empire (2009) is probably one of the best ways to first familiarise yourself with the huge timespan that is Byzantine history.
Averil Cameron, The Byzantines (2006) is another excellent introduction to the entirety of Byzantine history.
There are quite a lot of books that go into further detail about the different periods of Byzantine history but for the start those two general introductions should probably suffice. Of course you can always ask for more. I hope this helps!