The construction of the portable spectrometer, MULTI, is designed for the measurement of β-γ-neutron coincidences on beams of radioactive exotic nuclei. It will be used in measurements of the β-decay process of neutron-rich nuclei with large Qβ values accessible in radioactive beams facilities. The experimental technique includes the measurement of the ratios between gamma-ray emission and multi-neutron emission, following beta-decay of radioactive nuclei implanted into an active target. The construction of a gamma-ray spectrometer based on high-volume CeBr3+NaI(Tl) phoswich scintillation detectors is introduced. Results of the measurements of its fundamental characteristics – total detection efficiency, peak efficiency and Compton suppression effect with a 60Co source are presented. Design of the neutron counter array, consisting of 40 proportional counters filled with 3He gas, was optimized with Monte Carlo simulations. Results were validated with a 252Cf spectroscopic source, leading to expected detection efficiency of ∼35% for neutrons with energy < 1MeV. Further development plans are discussed.