How to connect sink, dishwasher and washing machine with single water supply?
I find it's best to assume the last guy had the same problem you are now having, and what you see is his solution.  

It looks like it was factory made as a double tap, with an outlet on top and bottom, and the top one was never used (or his fitting did not need tape).  From the bottom tap, the last guy put a splitter on it, to get 2 outlets from the one tap (while strangly not using the upper tap at all).

Behold 3 taps for you.

I don't think this is a tub/shower diverter, the valve angle is wrong, and that would be rather strange since there's no hot/cold mixer and it would be out-of-place in this location.