That’s not really so impressive. I believe the sun never sets on the remaining British protectorates now.
Never mind us Brits cheating with protectorates and such. I’m pretty sure it never sets on the republic of France itself. (French Guiana, say, is legally as much part of France as Provence.)
Arguably more like two - from 1206 ( Genghis unites Mongolia ) to 1262 ( his grandson Mongke dies in 1259, civil war commences in 1262 over disputed succession ). It saw three more or less orderly successions and as noted that is considerably more than Alexander accomplished :).
At any rate empires aren’t necessarily defined by stability. My namesake built an empire, but it was as ephemeral as Alexander’s, partially ( but not completely ) collapsing on his death. Alex had the lasting effect of the Age of Hellenism, the Timurids would go on to found the Mughal state with all its glories in India. But neither ruler really laid ground to secure the fortunes of their dynastic lines.