Biological impedance (BioZ) is an information-packed modality that allows for non-invasive monitoring of health and emotional state. Currently, most research involving tissue impedance is based on bulky or fixed-purpose hardware, which limits the scope of research and the possibilities of experiments. In this work, we present HEEPidermis: a System-on-Chip (SoC) which integrates all the blocks needed for tissue impedance measurement, including two 8-bit, arbitrary-signal current DACs, two VCO-based ADCs, and a RISC-V CPU to enable on-chip feature extraction for closed-loop operation. An event-based sub-sampler improves storage and energy efficiency for long-term recording. In addition to the versatile SoC, the digital back-end and behavioral models of the analog front-end are open-source, allowing fast system-level simulations or repurposing. The SoC was taped out on TSMC 65 nm LP process.