1 switch for 4 circuits
If I understand the question, I believe you could use a simple johnson counter IC which switches through a number of circuits for each pulse sent to the signal pin.  A decade counter (such as a 4017), for example, allows you to sequentially change among ten separate circuits sequentially. 

The image shows a simple example circuit that uses all ten outputs. You will have to modify it to do what you are asking. For example, you could shorten the sequence to four by connecting Q4 to the ICs RST pin so that every fifth pulse resets it to the first circuit. You'd have to check the specs for the particular IC you choose to use to see exactly how to do that.  

I don't mean to imply that this is the best circuit or the best chip to do the job, but you could look further into the idea of using Johnson counter ICs to help you accomplish what you want.

As pointed out in the comments you would have to debounce the switch also.


(source: iamtechnical.com)