I wouldn't keep it more than a week. Regardless, when Mozarella is heated during making it kind of pasteurizes it if it's hot enough. If you cultured it naturally it will last longer because of the competition effect from your cultures vs bacterial growth. If you used acid instead (citric acid, vinegar, lemon juice, etc.) than you won't have that effect.
In any event, Mozzarella is not meant to be aged and this is not aging. This is just shelf life.