Why do you think Bi-Wiring improves the sound ?

With one set of binding posts on the speaker end, in theory, unless you are modifying the connections to/thru the crossover, the only benefit would be thicker wire.  If the speaker has 2 sets of binding posts, and they give you a choice of paths through the crossover, then some changed response is possible.  However, dedicating copper to frequency bands leads to less than optimal use of the copper.  At some points in time the base may need a lot of energy from the amp and it cannot make use of the lower resistance that a common thicker wire would provide.

I think there are potential downsides of biwiring. The speaker designer (assuming they are competent) went to great pains to develop a crossover that effectively splits the signal between drivers, assuming the SAME SIGNAL on the inputs to the two parts of the crossover. Anything that might result in a different signal on the two input connections is going to defeat this design effort. 

Now, I suppose, if you prefer the sound from two separate connections to the speaker, then that's really all that counts. But if you are asking a theoretical question, I'd stick with a single connection to the speaker unless it was specific engineered to use an active crossover with biamping.

@bigkidz   Peter external shotgun biwire AQ Type 6 headed your way :-) I am guessing Tuesday you should have them to listen to :-))))) music is the gig - have fun

@gasboses 
Blue and chrome go together - 'chrome to get you home!'

I think it depends on speakers ... I have had Quad Kef, Falcon LS3, PMC and now Tannoy. 

The biggest difference is the Tannoy speakers where it was immediately clear almost like jumping up a model. On the rest it has been marginal and sometimes pretending to yourself it made a huge difference. 
So borrow some wire - try and then decide.

Out of interest my Harbeths had one terminal as it is something the designer thought worked and there was definitely a fashion for biwire speakers at one point that wasnt always sonically warranted except buyers demanded it and manufacturers supplied ....