The CONUS+ experiment aims to detect coherent elastic neutrino-nucleus scattering (CEνNS) of reactor antineutrinos on germanium nuclei in the fully coherent regime, continuing on this way the CONUS physics program started at the Brokdorf nuclear power plant, Germany. The CONUS+ setup is installed in the nuclear power plant in Leibstadt, Switzerland, at a distance of 20.7 m from the 3.6 GW thermal power reactor core. The CEνNS signature will be measured with the same four point-contact high-purity germanium (HPGe) detectors produced for the former experiment, however refurbished and with optimized low energy thresholds of about 160 eVee. To suppress the background in the CONUS+ detectors, the passive and active layers of the original CONUS shield were modified such to fit better to the significantly changed background conditions at the new experimental location. New data acquisition and monitoring systems were developed. A direct network connection between the experiment and the Max-Planck-Institut für Kernphysik (MPIK) makes it possible to control and monitor data acquisition in real time. The impact of all these modifications is discussed with particular emphasis on the resulting CEνNS signal prediction for the first data collection phase of CONUS+. Prospects of the planned upgrade in a second phase integrating new larger HPGe detectors are also discussed.