Can you raise a city center or district above level 2?

Solution 1:

As of 2014-11-09, it is not possible to upgrade a district or city center beyond level 2. I've tried the Vaulters and the Broken Lords in several cities each, but without success, and I don't expect other playable factions to behave differently. By the end of my games a missing science breakthrough can't have been an issue as well because everything except the win conditions in the last circle was researched.

Here are some city layouts that should work but don't (the expected 3's came out as 2's every time):

     1 2 1          1 2 1               1 2 1
    1 2 2 1        2 2 2 2             2 3 3 2
       3      or  1 2 3 2 1  or even  1 2 4 2 1
    1 2 2 1        1     1             2 3 3 2
     1 2 1                              1 2 1

It doesn't matter if the expected level 3 district is the city center or a built district.

Edit: I have verified (thanks to the anonymous suggestion) that the Cultists faction can have level 3 districs and city center. One turn after capturing their city with the Vaulters, all their level 3 districts downgraded to level 2. Maybe this is on purpose, after all the Cultists are limited to just one city.

Edit: I have verified playing the Cultists that their districts can reach level 3 but not higher. My city had several level 3 districts, none of them would rise to level 4, though.