We present and discuss a set of systematic measurements, carried out with gaseous proportional micro-pattern detectors, in order to assess their maximum gain when irradiated with high-rate soft X-rays and heavily ionizing alpha particles. The inventory of detectors tested includes: microstrips, micromegas, micro-dot, gas electron multiplier, CAT (compteur à trous), trench (or groove), micro-CAT (or WELL) detectors, as well as systems with two elements of gaseous amplification in cascade. W e confirm the general trend of all single-stage detectors to follow Raether's criterion, i.e. a spontaneous transition from avalanche to streamer, followed by a discharge, when the avalanche size reaches a value of a few 10 7 ; a noticeable exception is the micro-dot counter holding more than 10 8 . In multiple structures, where the gain is shared between two devices i n cascade, the maximum overall gain under irradiation is increased by at least one order of magnitude; we speculate this to be a consequence of a voltage dependence of Raether's limit, larger for low operating potentials. Our conclusion is that only multiple devices can guarantee a sufficient margin of reliability for operation in harsh LHC running conditions.