The universal problem of growing cities is not unique, no matter if it is in the sky
Have a look at Barcelona: The old medieval quarter of the city had planning principles (or rather lack of planning) that prevented its growth, new development in the modern era favoured matrix style planning (a universal grid) to accommodate extendable development, which you could see very obviously in an overhead image:
However, this also has drawbacks, with transport across matrices being slow. However it is by far the most flexible arrangement for growth. Most cities, such as Melbourne have matrix grids mixed with LA-style overlays of highways to cater for problems of transport.
In your situation the issues would be the same - however the advantage is that you have 3 dimensions to play with instead of 2 - with the ability to have either multiple layers of matrixes, or a 3 dimensional matrix structure. Study of the implications of this would be fascinating, and likely be based on nodal forms of development (such as activity centres and connections)
Your structural system might be nodal therefore to follow this, with large and small networks integrated either in a layered or evenly distributed matrix, or a combination of both. Each point could support others, reinforced as necessary. I would imagine not requiring much more than a network of steel cables would be needed dependant on maintenance and cost requirements (and of course: weight). Similar to nodally supported tensile rope playgrounds.
To support rigidity, the use of trusses would assist - replacing tensile members as you go. This would require constant engineering expertise to look at the whole structure, but would allow your city to grow organically without too much weight added and disturbing the overall structure too much:
Of course there are many other considerations for your city:
- Sewerage and waste
- Supply of essential food and water
- Servicing of commercial areas (ie, delivery networks, commuting)
- Residential value, where are the more expensive areas, what do they look at and how are they connected?
- Maintaining the value of such a city to justify the expense required to sustain it
But these can be fleshed out in other questions...