I recommend having a look at this document: it gives you quit good details:
Transpulmonary pressures and lung mechanics with glossopharyngeal insufflation and exsufflation beyond normal lung volumes in competitive breath-hold divers -- Loring et al. 102 (3): 841 -- Journal of Applied Physiology
A previous similar study by G. Simpson, J. Ferns, and Stephan Murat concluded that packing paradoxically does not increase the transpulmonary pressure, but the above mentioned study demonstrates the opposite, and claims the older one is inconsistent with pulmonary mechanics.
The measured values are quite individual, but one measured subject was able of packing more than 4 liters above his TLC (to 181% of his predicted TLC). The measured water vapor pressure raised from atmospheric 64 cmH2O to 80 cmH2O - that's increase of some 30%. At this subject though, pneumomediastinum (lung damage) was diagnosed. Usually, when packing, the percentual increase of TLC, and hence of the pressure is lower than that.
Roughly half of the packed air expands the lungs beyond their TLC volume, and the rest increases the pressure. What is more important though from the practical point of view for the theoretically achievable breath-hold time, is not really the pressure inccrease, but rather the increase of oxygen stores - at the measured subjects (all competitive freedivers) the increase was between 32% and 79%, which is rather huge, but on the other hand you have to keep on mind that packing has also negative effects - besides the risk of lung squeeze at depth disciplines, it may suppress or delay the diving response, increases the heart rate, adds to discomfort and muscle tension, etc. So although the oxygen stores are considerably higher, its consumption may rise considerably too, hence the outcome is usually lower than the theoretic numbers indicate.
PS: more interesting documents on packing can be found here:
packing @ APNEA.cz
