Lots of good suggestions here. I just want to chime in to reiterate that there's at least two different acoustic issues at play here. Absorption, including reverberation i.e how 'live' a room is and overall noise levels inside the room, is generally controlled by having lightweight but porous surfaces to prevent sound from bouncing off of hard surfaces. Examples are the mineral fiber panels in a t-bar ceiling, carpeting instead of laminate floors, and fabric wrapped or foam acoustic panels on walls. To simplify, these measures generally dampen sound transmission within the room.
However, the main issue here seems to be transmission through the structure to an adjoining space. In this case, mass and resiliency are our friends. The idea is to keep the energy of sound waves from travelling through the ceiling/floor/wall assembly. This is why condos with concrete floors rather than wood framed structures are quieter. To retrofit this apartment properly, I think you'd need to take down the existing ceiling, fill the joist spaces with friction fit mineral fiber insulation, and even mount a new drywall ceiling on resilient channels. Multiple layers (i.e. two 1/2" or thicker) of drywall will help provide some mass, and the resiliency of the metal channels absorbs the energy of sound waves, preventing it from travelling though to the space above. Not easy or cheap, but doing halfway measures probably won't give you the solution you're hoping for.
Also ensure that mechanical ducts aren't connecting both spaces. It's possible that one duct run supplies air to both the suite and the main living area, and sound is travelling down the duct unimpeded. If so, there's acoustic baffles that can be added to ducts. Any other flanking paths or openings need to be sealed as well.
Finally, and completely randomly, you could do what a friend of mine does...she lives close to a school for the deaf and only advertises for tenants there. They don't mind her classical music, and she only hears the occasional clanking of pots in the kitchen. She did hook up a door bell and smoke detector with a flashing light to cover the life/safety factor.