I enjoy the ancient-history-but-with-djinn idea so much Im not sure if I would prefer a sequel to the trilogy or another prequel. Here's Bartimaeus' timeline on Stroud's website in case you haven't read it, it has so many interesting tidbits.

I would like to see Akhenaten and Nefertiti, partly because they clearly made a strong impact on Bartimaeus as he cant stop mentioning Nefertiti in particular (Barti clearly had a bit of a crush...) and also me just liking history I would love to read about the fantasy djinn version of ancient Egypt. It seems like the story is strong in Stroud's mind, we already have the outline of the story, it starts when Nefertiti gets Bartimaeus to get her the anklet, yet she seems to have a change in heart, all the way to when the high priests revolt.

The most likely prequel is Gilgamesh, how epic would the Epic of Gilgamesh be but with Bartimaeus in his swashbuckling prime? We know Gilgamesh was probably the first human Bartimaeus ever liked and he met him young. I imagine this could be an incredibly fun and adventurous book. Also Barti has hinted he was pretty damned savage in ancient times, not only would I love to see bamf Barti and a possibly different tone of book in the series, but we would be able to see firsthand how his character and morality developed over the millennia (what other fictional character gets that?).

It is unlikely we would get a whole Ptolemy era book since we have so many flash backs and the ending, we also already know how it affected Bartimaeus as a character. Though I would still love to read about Bartimaeus on the campaigns and simply more conversations between him and Ptolemy. Having Ptolemy die again though would be depressing, but I suppose bittersweet because we would at least know more about him.

If you could choose the topic of another prequel what period of Bartimaeus' past what would you want it to cover?