Using multiple 4 input multiplexers to get an equivalent 16 input multiplexer
You simply have to add another level of multiplexers.



What you have now is the left part of this circuit: 4 times four inputs, giving 4 outputs. Use a fifth multiplexer to select one of those outputs. Since you have 16 inputs you need 4 select lines (2\$^4\$ = 16). That's the A, C, D and E lines. Note that the four muxes at the left use the same select lines.  

If you want to select the input the arrow points to you'll have to set D = 1, E = 1, and for the right mux A = 0 and C = 1.  

The 74HC153 is a dual 4-to-1 multiplexer.  

edit
Supercat's tri-state buffers are an excellent idea (don't forget to upvote), and it came to me naturally when I was writing the edit to OP. The multiplexer solution needs a few more parts, but can be implemented in a CPLD, I'm not sure if they support tri-state logic internally. (They do for I/O.)