Sound proofing floor

Green glue appears to be the most commonly used adhesive in soundproofing projects. A friend has a Rives-designed dedicated room which used a lot of that stuff.

As someone has already intimated.....is consult with an Acoustic Engineer (not some builder who has done acoustic work).
Acoustics is a science (unless we try to design a Concert Hall where it becomes more of an art), and what may seem logical to the uninformed can often be disastrous.
Putting in another floor is a pricey exercise and you want to do it ONCE and CORRECTLY.

Most of the advice posted above would spend your money for little result.
Sound travels in 2 basic ways....STRUCTURE BOURNE and AIR-BOURNE.
The trick is....the air-borne can become structure-borne and vice-versa.
Unless you TOTALLY decouple your new floor from the old, the STRUCTURE-BORNE sound will travel through.
Only an Acoustic Engineer can visit your situation and advise on the possible solutions.

I concur entirely with getting consul from an acoustical engineer, I needed to hear that from members, thank you.

Please inform us of the acoustical engineers advice. It will be interesting to look at the cost benefit ratio. Without going into specifics your idea of a 2nd floor islolated from the 1st is 'very' effective and I think you will find this confirmed by the engineer. (My father is an engineer)