Abstract The Next Ion Medical Machine Study (NIMMS) is an umbrella R&D programme for CERN accelerator technologies targeting advanced accelerator options for proton and light ion therapy. In collaboration with the European programme HITRIplus, one area of study is slow extraction which is required to deliver a uniform beam spill for radiotherapy treatment. Several techniques use the third-order resonance to extract hadrons; these include betatron core driven extraction and radiofrequency knock-out. Flexible simulation tools using these techniques were prepared and initially benchmarked with results from the literature that used the Proton-Ion Medical Machine Study (PIMMS) design. The limits of the current PIMMS design were then pushed to evaluate its compatibility to deliver 10x higher intensity ion beams, and using increased extraction rates.