Layers.
Here's a reference. They are trying to sell you a service (installing soundproofing), but they do a better than average job of explaining what they propose to do. I have no affiliation with them. I just find them good reading. To summarize the insights from there:
While mass is helpful in creating acoustic (sound) isolation, it is not the only thing. That's why even a 6" (15 cm) thick concrete floor will not eliminate sounds from above or below. You want to create sound absorbing/reflecting transitions. Your concrete floor/ceiling only has two transitions: into and out of. Adding more layers will increase the sound reduction, particularly if you are careful about how you connect the layers to each other.
Distance is also helpful. Note that the reference has two foot (.6 m) deep ceilings and floors. If you want to combine that with a 6" concrete barrier, that's about five feet (1.5 m) vertical separation between rooms. Without the concrete barrier, you might merge them together a bit to get a three foot (1 m) separation.
Avoid holes. If you add a pipe through that vertical separation, the sound will go through the pipe and be almost as loud as if there were nothing there.
At each transition, you want to absorb or reflect the sound. Reflecting keeps sound from moving between spaces. Absorbing keeps sound from echoing in the space. Hard surfaces are better at reflecting and soft surfaces are better at absorbing.
If you are connecting two layers, you want to isolate them acoustically by allowing them to move independently. This can be done by putting something squishy between them or by allowing them to move relative to the connector.
In acoustics, you will often see references to viscoelastic materials. Both sound and heat are vibrations (sound as a coordinated wave and heat as random vibration). A viscoelastic material converts sound to heat. To work, the viscoelastic material (which is squishy) needs to be sandwiched between two rigid layers, e.g. drywall or plywood. It is possible to buy drywall that itself has viscoelastic layers internally.
Regular insulation will also have an acoustic benefit. It squishes and absorbs sound that tries to pass through it. It can help fill some of the distance between layers. Air also helps fill distance. A mixture of insulation and air is more effective than either alone (i.e. it is better to leave air gaps between the insulation and the surface than to entirely fill the space).
In the reference, they put the support members in grooved mounts. This allows the support members to move vertically relative to the grooved mounts that restrict them horizontally. Isolation again. Other systems will use clips for isolation. In the reference, they do that in the ceiling.
Sometimes, it is better to soundproof your neighbor than you. It's like Covid masks. You don't wear a Covid mask to protect you. Your mask protects others. The masks that others wear reduce your chances of getting Covid. Similarly, it is difficult to prevent sound from traveling from above you. It is far better for the neighbor to have a floating floor that swallows noise than for you to try to soundproof your ceiling. You'll get a better reduction from your neighbors efforts than from your own.
Soundproofing also needs to be omnidirectional. If you soundproof your ceiling but not your walls, sound from the neighbor can go into the walls and come out in your space. So for soundproofing to work, you want your ceiling, floor, and walls to all be isolated from their surroundings.
For walls, it's somewhat simpler. The acoustically isolated walls not only do not need to be load-bearing, they shouldn't be. You want them to be acoustically isolated from the rest of the structure. So you build acoustic walls internal to the walls of the overall space. You can even build separate doors and windows into the acoustic walls. This gives something of an airlock effect with doors. If you open both window layers, you lose the acoustic protection but gain a breeze. Close them and lose the breeze but gain acoustic protection.
All directions should have acoustic isolation from their surroundings.
Soundproofing has diminishing returns. It's not hard to get the first twenty or thirty decibels of reduction. The next twenty is much harder and it gets more difficult from there. If you add the full floor and ceiling options to a concrete slab, you can't add their acoustic stats. They add some improvement, but less and less the more that you add.
There are other alternatives. For example, sound masking can make it easier to live with your neighbors by adding some sound of your own. A white noise machine or an indoor waterfall can add sounds that many find pleasant that drown out the footfall or television noise from the neighbors.
Note that these attributes need to be designed into the building before construction commences. You can't add them to an existing building without reducing the height of the room. You need that space to be part of the architectural plans. It's not something you can do afterwards as a do-it-yourself home improvement project. There are less effective options if you're stuck with trying to do things after building, but those aren't what a new construction apartment building would do.
