No, you can't retune a set of strings by an octave. There are several ways to do what you want to do however:
1) And I think this was the intent of your first response above, use two sets of strings and re-string according to what you will be playing that night. This is fine for night to night use but if you need to change tunings back and forth in a single night it would be too cumbersome.
2) Pick a tuning and stick with it. On a traditional EADG bass half the E string, ~two thirds of the A string and all or nearly all of the D and G strings are in the same range as a regular guitar anyway. You probably spend a good bit of your time in the regular guitar's octave already and solo guitarist can play very effective bass lines in that octave. So can you. You can differentiate yourself from the other members of the ensemble by what you are playing even if it is in the same octave as they are. Or stay with the lower tuning and just do your solo work farther up the neck, if that works for you. Compromise "baritone" tunings might also work for both purposes. Tunings like GCFBb, ADGC, BEAD, and DGCF will give you a little of each world in different blends between the two. A final variation of this approach would be to buy a second ABG and tune one to each tuning.
3) Retune a single set of strings up and down, just not by an octave. The Hipshot Bass Extender tuners work pretty well over a limited range, especially if the string gauge is chosen as a compromise between the two tunings. You can use a set of light gauge bass strings to tune between EADG and GCFBb for instance. If you custom select a set of strings for GCFBb you can probably even tune them over a fourth, EADG to ADGC. And there are many other possibilities....