After playing a lot of EU4, this idea came into my head.
Counting vassals, clients, and puppets, how far west can the Timurids get, with a POD no less than 1350?
An idea I had, is that they could possibly expand from Persia to Northeast Arabia (although it might be hard).
If by Northeast Arabia you mean Kuwait, it did span over that territory in OTL under Timur. So in case that is what you mean, a quick list of the lands the Timurids ruled at their height:
Transoxiana, Khwarezmia, Ferghana, Badakhshan (All of the modern Central Asian republics except Kazakhstan), with it's border somewhere around the Kyzyl Kum, perhaps as far north as the Jaxartes (Syr Darya)
Persia, Baluchistan, Khorasan, Azerbaijan, Iraq (Modern Iraq, Afghanistan, Iran and most of Pakistan west of the Indus river)
Armenia, Georgia, Dagestan, Kurdistan (everywhere as far west as the border with the Mamluks in eastern Syria and an area roughly equivalent to modern Kurdistan being their western border).
OT: I think the Timurids at best could hope to expand further into India during their wars against the Delhi Sultanate, and further west into Anatolia, best case scenario causing the Ottomans to fall apart and the various Beyliks being subjugated as vassals but not losing their independence entirely.