What's the maximum number of planets that could orbit the sun?

I think that trying to maximize the number of "livable" planets might work out best if the planets were different sizes in different orbits. Planets closest to the star might need to be able to lose heat more easily than planets farthest from the star in order to maintain Earth-like temperatures with Earth-like atmospheres. Of course, the atmospheric pressures and surface gravity levels would be different, too. But, animals, even humans could evolve to accommodate those differences. Launching space vehicles from their surfaces might be substantially more problematic from larger planets with deeper gravity wells and thicker atmospheres, but for a society that can build and position planets at will, that would not likely be a problem for them.
 
Mar 8, 2022
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The 'ring of pearls' looks like one good option.

I wonder if having a deeper atmosphere would help keep more distant planets warmer?
Using a really strong magnetic field maybe?

Twin planet pairs could shade one another to keep them cooler? Sort of a major eclipse on a regular basis?

Or several large moons synchronized for stable orbits for a similar shading effect?
 

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