3 Way Light Switch on Stairs
Smart switch; change one cable

The cable from the existing lamp to the nearer switch (upstairs?)... you need to change that to a /3 cable (red white black).  

You can extend the cable to your new lamp from any switch box.  When you do, use colored tape to re-tag the black wire as a red wire.  

Now we're going to fit smart switches that allow wireless connection of remotes.  These smart switches cannot require a wire for comms between them, as we lack any spare wires. 

Now we're going to change the color codes.  As it happens, the existing color codes will suffice in all locations: 


black = always-hot
white = neutral
red = switched-hot


Your master smartswitch attaches to black, white and red. 

Your remote smartswitch attaches to black and white only.

Your original lamp connects to red and white. 

Your new lamp attaches to red and white in the box nearest it.