First, you can't really "soundproof" anything and we should be discouraging this misuse of terminology. More appropriate to be looking to
address sound isolation.
What that means then depends upon the situation. What are the noise sources? What levels are acceptable at the receiver/listener? You have to determine the
level and frequency information for both the source and receiver to establish what sound isolation is required. You may also have to consider the
effect of the environment on those levels.
Knowing what sound isolation is desired, you can then start to look at what isolation you may already have and what improvements may be necessary. You may also have to
address practical considerations such as what construction is physically or budgetarily feasible. You may find yourself going back to the previous step and making compromises in the acceptable levels at the receiver or controlling the source levels.
When usually also has to consider the implications of issues such as other construction and flanking paths on the isolation possible. For example, to really get the isolation desired you might find that you get the window to where the rest of the wall or shared ductwork or other concerns become limiting factors. You may even have to watch out that what you do doesn't make things worse, it is possible to do things that would appear to help but could actually make things worse.
The
point here is that you need to start by identifying the noise source and what goals you are looking for as far as the received levels. It is a big difference between wanting to just get what you can and needing to achieve some specific result, even if just to justify the effort. You also have to provide a little info on the existing construction and any
practical, physical or budgetary limitations. While some improvement is most certainly possible, it sounds like you will likely be very limited in the improvements that are possible.
There also seem to be some basic misconceptions presented. Absorption such as
insulation, acoustic tiles and carpet is not usually effective for sound isolation, absorbing sound is different than preventing transmission of sound. Absorption may be used as part of sound isolation systems but is usually a poor sound isolation solution by itself and is quite limited in what can be achieved, especially at low frequencies.