Three way light switches in a tower
As Wolf says, a combination of SPDT and DPDT switches. One switch on each floor, top and bottom are SPDT, all others are DPDT. The number of switches is one more than the number of lights. Here are a couple of ways to wire it:



The left diagram shows the sane way. Blue is the neutral leg.

The right diagram shows how to use the Carter three-way pattern to save copper. I think this is now banned throughout the civilized world because sometimes when a lamp is off it is hot on the shell side. It requires turning off the entire circuit at the service panel to safely change a light bulb.

EDIT 2/4/16: The actual requirement is for two lamps to be controlled by each switch. I think that the stairway should be usable serially in the same direction (the accepted answer only allows descent after ascent). Here are a couple of ways to wire it:



The left diagram shows the safe way. Blue is the neutral leg.

Note that, except for the lowest and highest floors, it is not possible to control a lamp on the same floor as the switch. I'm sure this can be done with an additional switch on each floor. However the instructions for using the switches will become too confusing for most users. And I am drifting away from the core subject of this SE.

The right diagram shows the functionality of the left diagram, implemented in the Carter system. Note the remarkably reduced number of wires and switch contacts. Remember, this method is very dangerous. You might get electrocuted maintaining it, you might lose your license for building it, and you might get downvoted just talking about it.

This pattern, and other too-clever circuit solutions, often find application in low-voltage, signalling, and railroad block controls. It is not used in residential structures, which are typically required not to kill their occupants.