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You could build them all at the same time if you wanted to!
However, you cannot build multiple in the same system, as they would collide with eachother.
If you are asking if I can make a version that has more sections...
Maybe.
I honestly had a hard time getting this one to work with the orbital angles so that they would all show up in the right places. It turns out it was quite easy.
Each set (of 3 sections) has 3 orbit angles; one for each section, and it goes as so:
Section A-1 Orbit angle: -30
Section A-2 Orbit angle: 0
Section A-3 Orbit angle: 30
They are all placed at Orbit Distance (distance from the center of the system): 45.
To make a Ringworld with, say, 30 sections, would require to increase the Orbit Distance. Increasing the Orbit Distance requires to lower the Orbit angles. I have not figured out what math is involved in this quite yet.
Also, each section is model, similar to ships and stations. They are all created to work together to form a circle. If you make that circle larger, and add more parts, you have created a clover of sorts, not a circle.
I persoanlly do not like this look on Ringworlds, but I lack the knowledge to make new models with less curve.
Take this image for example:
https://i.imgur.com/9xJBpOP.png
The inner circle represents a default Ringworld. The diagonal red lines show where the edge of each set is. The outer circle is comprised of completely of the same sets as the inner ones, but doubled. Notice how it is no longer a circle? That is exactly how it would show up in the game, though.