Abstract Multiple-lift absorption cycles are an interesting option for cooling and refrigeration driven by waste or renewable heat. Compared with single effect cycles, they allow higher thermal lift or lower thrust, but they often require the use of controlled valves, which can cause stability and control issues. The self-adapting concept, firstly introduced in the two-pump series-flow double-lift cycle, replaces the valve with a phase separator, overcoming this drawback. In this work, five new cycle layouts, incorporating the self-adapting concept, are presented: the one-pump series-flow double-lift cycle and four triple-lift cycles. The cycles are compared in terms of COP and heat duties under various conditions, using NH3 H2O and NH3–LiNO3 as working pairs. It is found that the double-lift cycles have a COP in the range 0.35–0.20, about 0.1 higher than the triple-lift cycles. However, triple-lift cycles accept cooling water temperature up to 8 °C higher. Cycles with multiple pumps have higher efficiency than single-pump cycles, especially at high lift conditions. The use of NH3 H2O as working pair guarantees higher COP at low thermal lift, while NH3–LiNO3 has wider operating range and better performances at high thermal lift.