We propose a channel estimation and joint beamforming design method for multi-IRS multiple-input and multiple-output (MIMO) systems. We investigate the scenario where multiple intelligent reflecting surfaces (IRSs) are located on the exact spot of the channel scatterers. We investigate the spectral efficiency (SE), benefits and drawbacks of deploying multiple IRSs in comparison with a scenario with a single or no IRS. Our simulation results show a trade-off between the number of reflecting elements and the total number of IRSs in the system.