Is there something like a Single Pole Quad Throw Relay?
There is a family of relays known as stepper relays. They sequentially allow connection of an input to some number of outputs. They used to be used in the millions by the telephone company for connection of telephone calls on the basis of dial pulses created by a rotary dial telephone.

These days you may be best off selecting a suitable small relay that meets your signal carrying capabilities and then using multiples of them to create your selector. 

You did not say anything about your signal characteristics. Maybe you could share that information as there may be folks here that know of suitable solid state switches that may work.