Second kombucha fermentation imply most of thje time a bottled up fermentation with a special lid to let the gas escape under a reasonable pressure, this imply :

• A carbonation with whatever O2 is left in the liquid and at its surface.
• A diminution of the sugar content.
• A generation of alcohol.
• An increase in acidity.

Depending on many parameters the end product will have different values concerning the four main parameters, with very long time bottled up tending to standard CO2, almost no sugar and the acidity tipping in favor of alcohol content. Great care must be taken to avoid contamination, basically:

• High hygiene and all used gears in close previous contact with boiling water.
• A kombucha acid enough acid enough to avoid risk of botulism.

Anyway, it's quite advanced kombucha techniques, I wouldn't use it for health reasons, because I don't see why it would work better than standard kombucha, except that low sugar content is good, but high alcohol not so much and because of adaptation to low oxygen conditions. So caution is very important.. By the way if you try kombucha for health reasons, I thin milk kefir if much better, at least I experience it like that, but I should note that my experience is a bit biased, because when I tried kombucha I could probably never tell if it would work because I was already in full shape.

By the way I am not an expert in kombucha especially not the bottled up sort, even if I mage a few trial with one exploded bottle : not enough gas on the top so the water could not escape through the rubber seal, the pressure increased and the bottle exploded silently, not enough gas to make a big catastrophe, the bottle parts were still in position, but the glass was broken!