The Xe(L) system at λ ~ 2.9 Å uniformly exhibits all of the canonical attributes of a strongly saturated amplifier on the full ensemble of single-vacancy Xe^q+ transition arrays (q = 31, 32, 34, 35, 36) that exhibit gain. The key observables are (1) sharp spectral narrowing, (2) the detection of a narrow directed beam (δθ_x200 µrad), (3) an increase in the amplitude of the emission and the development of an intense output (≥10⁶ enhancement) and (4) the observation of deep spectral hole-burning on the inhomogeneously broadened spontaneous emission profile. Experimentally determined by two methods, (a) line narrowing and (b) signal enhancement, the observations for several single-vacancy 3d→2p transitions indicate a range of values for the effective small signal (linear) gain constant given by g_o25−100 cm⁻¹. Quantitative analysis shows that this result stands in clear conflict with the corresponding upper bound g_o40−80 cm⁻¹ that is based on available spectroscopic data and estimated with conventional theory. Overall, the observed values deviate substantially from expectations scaled to the spectral density of the measured Xe(L) spontaneous emission profile; they are systematically too high. The most extreme example is the heavily saturated Xe³²⁺ transition at λ = 2.71 Å, a case that fails to reconcile the lower bound of the measured signal strength with the corresponding theoretically predicted maximal value; the former falls above the latter by a factor exceeding 400 giving an enormous gap. Moreover, although saturation is a prominent characteristic of the amplification at λ2.71 Å, as demonstrated by spectral hole-burning, the theoretical upper bound of g_o given for this transition is far too small for saturation to be reached. The Xe³¹⁺ transition at λ2.93 Å exhibits comparably pronounced anomalous behaviour. This double paradox is resolved with the Ansatz that the amplification is governed principally by the saturated gain g_s, not the conventionally described small signal value g_o. This interpretation is further supported by the observation of deep spectral hole-burning, the signature of strong saturation, that occurs uniformly across the spectrum of the spontaneous emission profile. The effective amplification exhibits an anomalously weak dependence on the spectral density; saturation is the rule, not the exception. A lucid manifestation of the saturation is the recording of spectrally resolved x-ray yields on the Xe³¹⁺ array that are sufficiently high to produce gross structural damage to the material in the film plane of the spectrograph. The behaviour of the amplifier can be best described as an explosive supersaturated amplification. The source of this exceptionally strong amplification can be traced to the dynamically enhanced radiative response of the excited Xe hollow atom states located in the clusters that are mode coupled to the plasma waveguide forming the amplifying channel.