Secondary ice production (SIP) has an essential role in cloud and precipitation microphysics. In recent years, substantial insights were gained into SIP by combining experimental, modeling, and observational approaches. Remote sensing instruments, among them meteorological radars, offer the possibility of studying clouds and precipitation in extended areas over long time periods and are highly valuable to understand the spatiotemporal structure of microphysical processes. Multi-modal Doppler spectra measured by vertically pointing radars reveal the coexistence, within a radar resolution volume, of hydrometeor populations with distinct properties; as such, they can provide decisive insight into precipitation microphysics. This paper leverages polarimetric radar Doppler spectra as a tool to study the microphysical processes that took place during a snowfall event on 27 January 2021 in the Swiss Jura Mountains during the ICE GENESIS campaign. A multi-layered cloud system was present, with ice particles sedimenting through a supercooled liquid water (SLW) layer in a seeder-feeder configuration. Building on a Doppler peak detection algorithm, we implement a peak labeling procedure to identify the particle type(s) that may be present within a radar resolution volume. With this approach, we can visualize spatiotemporal features in the radar time series that point to the occurrence of distinct mechanisms during different stages of the event. By focusing on three 30 min phases of the case study and by using the detailed information contained in the Doppler spectra, together with dual-frequency radar measurements, aircraft in situ images, and simulated profiles of atmospheric variables, we narrow down the possible processes that could be responsible for the observed signatures. Depending on the availability of SLW and the droplet sizes, on the temperature range, and on the interaction between the liquid and ice particles, various SIP processes are identified as plausible, with distinct fingerprints in the radar Doppler spectra. A simple modeling approach suggests that the ice crystal number concentrations likely exceed typical concentrations of ice-nucleating particles by 1 to 4 orders of magnitude. While a robust proof of occurrence of a given SIP mechanism cannot be easily established, the multi-sensor data provide various independent elements each supporting the proposed interpretations.