The question is ambiguous. There's the literal meaning of "juggle," which is to repeatedly toss bottles into the air and catch them, made all the more impressive if the number of bottles exceeds the number of limbs used for the task.
But there's also a figurative meaning, as it pertains to wine bottles. One who has several bottles open at the same time might be said to be "juggling" them as they alternate drinking glasses of wine from them.
The correct answer for me in the former case is 3 (or 4 or 5, depending on what 'tricks' are employed).
The correct answer for me in the latter case is: dozens. Hundreds, maybe. Though it would be a shame to have so many bottles opened but unconsumed.