The construction of new portable spectrometer "MULTI" is designed for the measurement of β-γ-neutron coincidences in search for pygmy dipole resonances in exotic nuclei. It is based on many years of experience with spectrometer for direct measurement of the total reaction cross section with radioactive beams. Experimental technique includes measurement of the ratios between gamma-ray emission and multi-neutron emission, following beta-decay of the implanted radioactive nucleus. The spectrometer consists of an in-beam multi-detector telescope for identification of the secondary beam projectiles and a gamma-ray spectrometer with neutron counters array, surrounding the β-detector. The in-beam part consists of active collimators, silicon dE0 detector for particle identification by dE:TOF (time of flight) method and β-detector for implantation of the nuclei of interest and measurement of electrons emitted in β-decay. Gamma-rays and neutrons are measured by eight CeBr3+NaI(Tl) phoswich scintillation detectors, surrounded by 40 neutron counters in form of 3He tubes in polyethylene blocks. The design was optimized with Monte Carlo method in Geant4. Data acquisition electronics is based on the digital pulse processing modules in VME standard, including pulse-shape analyzing techniques for identification of the particle type. Project and construction of the spectrometer, calibration measurements of its fundamental characteristics and the method of measurement with radioactive beams will be presented.