I would recommend adding a small additional system for the third level.
How to keep the third floor cool.
If you get some exterior roller window shutters for your top floor and keep them closed during the day to block the sun that might help to keep it cooler upstairs.
Your first step should be to get that 3rd floor room better air sealed and better insulated and go from there.
This relatively new technology is extremely quiet comfortable and energy efficient.
Placing a cold wet washcloth on your neck or wrists drinking something ice cold to stay hydrated using mint or menthol.
Central air for a third floor first of all adding new ductwork to your home is expensive.
The floor of the 3rd floor room is likely totally connected to the attic without any air seal or insulation separating the 3rd floor room with the attic.
Consider having yours insulated or replaced with sealed double insulated windows that have special layers to block much of the heat gain that comes in through windows.
Keep the blinds curtains upstairs closed or at least close the blinds on the side of the house the sun is shining on.
What if you want all areas heated or cooled simultaneously.
This will keep the sun from heating the top floor even more.
An answer without a question is meaningless.
Unfortunately none of these are ideal.
Windows on second and third floors can add a lot of light and character to your home but they can also let in a lot of heat too.
Wearing lightweight loose fitting clothing taking a cool bath or a cold shower.
Extend ductwork up there to connect the central ac.
Or use a window or portable air conditioner.
A less expensive option would be to install a window air conditioner unit.
Not if the thermostat is on the 3rd floor thus making the ac run constantly because it is hot up there so yes keep it cool so that your 1st floor is not freezing because some dumbass put a thermostat on the top floor.
Be sure not to close off too much downstairs as you will risk freezing up your system.
The most ideal option would be to look into a ductless hvac system.
Place a large fan at the base of the stairs the floor below main floor and position it to blow air up the stairs.
By splitting to force air to the third floor you are removing from another area.
If the thought of getting into a cold bath makes you sweat fill it first with.
In the evening and night you can open the shutters and windows to let in fresh air.
Keep a cool bottle just beside your bed and drink it in the night whenever you will feel warm and humid.