Radiation toxicity is a major factor limiting therapeutic doses in oncology. Inspired by Yonezawa’s studies of radioadaptive survival in mice, we adopt an empirical approach because the complexity of the human body makes comprehensive biophysical analysis currently impractical. Even complete knowledge of cellular interactions would not necessarily explain whole-system responses. A previously developed model described adaptive biological responses to time-dependent irradiation using a damped-oscillator analogy, but employed a limited set of response curves without a specific biological basis. The present study generalizes this model by introducing a biologically relevant inverted Gompertzian-like response shape, with potential applications in biology and oncology. The resulting model suggests that radiation training (priming) through low, gradually increasing doses of total-body irradiation could improve tolerance to subsequent therapeutic irradiation, potentially allowing doses up to five times those conventionally administered. Very preliminary estimates based on the existing evidence indicate a training period of approximately six weeks and a cumulative priming dose of up to about 600 cGy (such a dose is lethal if given acutely—but if fractionated over several weeks, even without the assumed adaptive protection, it should not cause acute effects). If validated in animal models and subsequent clinical trials, this approach may significantly enhance the effectiveness of radiation therapy by enabling the safe administration of higher therapeutic doses.