The soft tiles you mentioned in your drop ceiling provide some insulation, but if you want more I think your only option is to install fiberglass batt insulation above your drop ceiling.
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Oh no....you have many more options than fiberglass batts.
Firstly, you either want soundproofing or you want cheap NON-soundproofing.
Remove all the drop-in ceiling tiles.
If you have a concrete slab above you need to attach 3"x2" wood battens to it through special rubber insulators. Then fix 3" fibreglass insulation between the battens before fixing 2 layers of 5/8" plasterboard (Fyrchek) to the battens making sure no contact is made to the walls at the ceiling junction. Fill this 1/4" gap with silicone sealant.
If you have timber joists above, the best way is to span a separate timber structure to support the same ceiling as described above.
Alternatively you can attach timber battens cross-wise to the joists again through special rubber insulators and repeat the ceiling structure above.
I just want to add one thing to the mix.
I tried to stop the music from the basement using fiberglass insulation and styrofoam sheets between the rafters, and then the acoustical ceiling panels to finish everything off.
I finished the whole basement and turned on the system. Guess what? The sound still came right through.
Breaking down what was happening, I found that the sound was coming up through the heating vents.
I used a product called Z brackets. As the name implies it is shaped like a Z. It is made of 18ga? metal. It basically de-couples the ceiling from the rafters. I had foam insulation sprayed in between the rafters and also sprayed the air ducts. Seemed to work very good for me, did not make it totally sound proof, but reduced a lot. My wife can now sit and watch TV which is above listening room and only has to turn the TV up a few DB.
There are a lot of new products out there that you need to do research on. It all depends on how much money you have for the project. The Handbook of Acoutical Engineering has some great information in it.
If your using the basic wire to hang the ceilings frame, add some type of mass like rubber to each wire. These carry a lot of sound vibration, sort of like the "string and can" phone. Experiment by just tapping on the wire, and clamp something on them that stops as much vibration noise as possible. I don't know if there is any commercial product for this. A friend even used lead fishing weights to help.