One of the most important things to understand about sound isolation in a building is that the sound isolation between two homes is not determined only by the common wall or floor. All the other parts of the construction can transmit sound.
In the figure here, a D indicates direct sound - sound coming through the common wall or floor. An F indicates flanking sound - sound traveling along some in parts of the building other than the common wall or floor. These are just some of the paths sound can take. They all combine to determine the total sound isolation between the apartments.
Flanking sound transmission can be very important, to the point that it dominates the combined sound transmission. If this happens, improving the common wall or floor may not significantly change the combined sound isolation.
In complicated situations, it may be worth hiring an acoustical consultant to advise on the best way to improve the sound isolation between homes.
When sound transmission is measured in a laboratory, there is, in principle, negligible transmission of sound energy along paths other than the direct path through the specimen. So laboratory STC values represent the maximum value of sound insulation a construction can provide.
During the design of a building, all possible flanking paths must be considered and steps taken to minimize their effect. Otherwise, the net sound isolation can be much less than that expected from laboratory testing. With good design of the junctions between walls and floors and the use of floating floors and resiliently supported wall and ceiling surfaces, flanking can be reduced so sound isolation ratings measured in the field are close to those obtained in the laboratory.