well....

Of course you can get everything guitar-wise. I´ve seen a 10-stringer classical on the frankfurt music fair 2 years ago and it looked cool but they didnt let me try it :(
looked like that one (which is an 8-string)

http://www.fineguitarconsultants.com/kurt.htm

However - the advantages should be obvious - a bigger tonal range.

More common than those are contra-guitars which dont have the additional strings on the same fretboard, but like a lute on a second fretboard.

Looks like this 15-stringer here:


These are used to perform simple bass-lines with. Most lute-music was written for those types of instruments. Thats why alot of lute music is way easier to play on a lute than on a regular guitar for you can play the bass notes without fretting them, thus making alot of chords easier to play. Plus the sound is very rich.
The contra-guitar has been invented in the 19th century in vienna. The tuning of the low bass strings is chromatic moving from Eb downwards. So on the biggest of those instruments the lowest note is a very low G.