Because of the way Civ processes city results at the start of a turn (in the order they were founded, starting with the capital), it is not possible to spawn a natural great person in more than one city on the same turn. So, if you have GPs in two or more cities who look like they should hit the next multiple-of-100-GP-points increment on the same turn, the one in your oldest city will spawn first, resetting the counter up 100 GP points. When the computer then processes the next city with a GP ready to spawn, you will be nearly 100 points away, so no spawn.
It is possible to get multiples in a single city on the same turn -- in a science game, if I don't take Order to buy a GE with faith, I will usually try to do a simultaneous GS and GE at least once a game if I can (e.g., when I'm pretty much done producing natural GSs and want to use a GE to bulb Hubble). But, make sure you won't have an "older" city spawn a GP on that turn ahead of the city where you are aiming for multiples. I won't hesitate to reassign specialists for a turn or two to slow things down in one city to allow another city with potential multiples to get to the finish line first.
None of this appears to apply to so-called "free" GPs (from, e.g., the Liberty finisher or Pisa) that you select at the beginning of a given turn, since those aren't awarded to you until you click on the "select great person" alert message (they do kick the GP counter up by 100, but not until you select them--in part because you have the option of selecting a GG, GAdm or GPr, which are subject to different counters). So, if you have Pisa being completed in one city, and a GP (or multiple GPs) about to spawn in another city on the same turn, you shouldn't have to worry about sequencing of the two cities.
On the other hand, for GPs awarded automatically upon completion of a specific wonder (such as GSs from PT or Hubble or GAs from Louvre), I think you do need to worry about city ordering, but it is confusing; the awarded GP may spawn outside your capital, but that doesn't appear to happen until the computer processes the city in which the wonder is being built. So, I think you should be OK if the wonder is being built in a "younger" city than the city in which you're trying to spawn multiple GPs, but I usually try to delay completing the wonder until the next turn to avoid finding out whether I'm wrong, wrong, wrong.
And I have no idea how GP "gifts" from allied CSs affect these mechanics. I prefer to avoid those, so I don't take that Patronage policy, if I can help it.
)
