Experiments on ASDEX Upgrade and other tokamaks have shown that the magnitude of mechanical forces and thermal loads during disruptions can be significantly reduced by raising the plasma density with massive injection of noble gases. This method should be applicable to ITER too. Nevertheless, the suppression of the runaway electron (RE) avalanche requires a much larger (two order of magnitude) density rise. This paper reports on recent experiments aimed at increasing the plasma density towards the critical value, needed for the collisional suppression of REs. An effective electron density equal to 24% of the critical density has been reached after injection of 3.3 bar l of neon. However, the resultant large plasma density is very poloidally and toroidally asymmetric; this implies that several valves distributed around the plasma periphery become necessary at this level of massive gas injection to ensure a homogeneous density distribution.