A low material erosion rate (MER) and a high roughness are challenges encountered when machining the biomaterials using the hydroxyapatite powder (HAp) suspended-electric discharge machining (EDM) process. Thus, a comprehensive analysis is needed as the required machining outputs are highly dependent on EDM process factors due to its stochastic behavior during the operation. In this context, the research aims at a detailed investigation of the EDM process factors on the machining responses and the feasibility of multiple additives mixed-EDM process needed for processing 316L steel to realize its full potential. To improve MER and reduce both surface roughness (SR) and tool erosion rate (TER), a hybrid of carbon nanotubes (CNT) and HAp supported EDM technique is employed. SEM and EDX analyses have validated the machined surface morphology and migration of the elements. The EDM process parametric optimization has been carried out utilizing Taguchi-based orthogonal design assisting to get the lowest both TER and SR of 0.245 mg/min and 1.85 μm, respectively. The highest MER of 26.47 mg/min as a machinability metric is achieved. Peak current, pulse-on time and HA/CNT quantity are found to be significant determinants in MER, SR and TER using the ANOVA method. The predicted best 21 solution sets using multi-objective spotted hyena optimizer (MOSHO) and following the set objective functions are tabulated. The estimated experimental evaluation errors are lower than 10, indicating that the predicted solution sets are highly accurate. This research offers a novel approach to process the 316L steel for biomedical applications with enhanced machining performances. © 2021 The Author(s)