Switches needed in an n-location multiway switching system
What you call &quot;three-way&quot; switches I'd call &quot;two-way&quot; switches because they switch one of two ways - just a minor thing really. The middle switch in the 3-location scenario can be made from 2 x 2-way switches but they need to be &quot;ganged&quot; so they both operate together: -

To make n-location switching you repeat the middle dual-switch circuit from above - two wires in and two wires out. Repeat n times. It's an Exclusive or function.
4-location switch: -

Is it possible to just use 1 x SPDT switch per position - I think not but i'd like to see it disproven