To me addition activated carbon is the minimum to compliment to the simple DI resin filter, below are some info for you to decide:
DI Resin: De ionization removes ions (heavy metals or salts) dissolved into the water.
RO membranes: Membranes remove bacteria, virus, metals, salts (ions).
Carbon Filters: Carbon absorb chlorine, chemicals and filter particulate matter.
Sediment filters: Sediments filter out particulate matter only.