I'm working on an Alien-esque pseudo-cyberpunk space station. My idea for the station was a classic O'Neill cylinder with smaller "sub-cylinders" at 90 degree angles along the sides, each rotating independently. The primary cylinder was once a typically idealistic colony though it is now run-down; the sub-cylinders are concrete jungles that were bolted on after the station was past its prime. What kind of problems do you foresee with this? Would the sub-cylinders throw off the centrifugal gravity?
If the main cylinder is still rotating, and taking the sub-cylinders along with it, the sub-cylinders will be completely uninhabitable.
As the sub-cylinders rotate, the effective gravity at any point on the sub-cylinder will vary between the sum of the spin-gravity of the sub-cylinder itself and that of the main cylinder at whatever main-cylinder radius the point happen to be, and the difference of those two. Additionally, the direction of the total effective gravity will appear to rotate as it varies in magnitude, such that most of the time it is not actually perpendicular to the ground, or anywhere close to it.
Maybe not Sub cylinders, but additional blisters on the skin of the primary cylinder.
The Rotation of the prime cylinder creates the artificial gravity (yeah, I know, it's all angular momentum and such, but artificial gravity is easier to understand for the layman). If you add another tethered cylinder, the "gravity" will be slightly higher at the furthest line from the center of the primary cylinder. That means if tethered cylinder is spinning, it's going to have very wonky and changing gravity on the inside. Will it be spinning fast enough that everything on the inside stays put? Also, why bother building something with the massive mechanical requirements to keep the sub habitat spinning.
A better option would be to build Blister environments on the outside of the primary cylinder. You would have to build them in balanced multiples at the same time in order to keep the main O'Neill cylinder from wobbling. Think in terms of adding lead slugs to a car tire's rim to keep it balanced. If it's a Blister type construction, you could patch into the environmental systems from the main cylinder, or not, depending on your story. Artificial gravity will be built in and will not need any addition mechanical resources.
The blisters could also be built in layers, like inverted skyscrapers, making your cylinder look kind of like a spiky dog toy. You will have a natural limit to how many layers, as the artificial gravity will be higher the farther out you go. Larger structures will also be more vulnerable to micro-meteor impacts and space debris.
So these fixed blisters give added space, away from the primary cylinder, without all the complications you would get from building a separate complete cylinder. Much lower material and mechanical costs, and nobody gets pasted to the inside of the hull due to wonky artificial gravity.