Vortex beams carrying orbital angular momentum (OAM) have gained much interest in optical communications because they can be used to expand the number of multiplexing channels and greatly improve the transmission capacity. However, the number of states used for OAM-based communication is generally limited by the imperfect OAM generation, transmission, and demultiplexing methods. In this work, we proposed a dense space-division multiplexing (DSDM) scheme to further increase the transmission capacity and transmission capacity density of free space optical communications with a small range of OAM modes exploiting a multi-ring perfect vortex (MRPV). The proposed MRPV is generated using a pixel checkerboard complex amplitude modulation method that simultaneously encodes amplitude and phase information in a phase-only hologram. The four rings of the MRPV are mutually independent channels that transmit OAM beams under the condition of occupying only one spatial position, and the OAM mode transmitted in these spatial channels can be efficiently demodulated using a multilayer annular aperture. The effect of atmospheric turbulence on the MRPV was also analyzed, and the results showed that the four channels of the MRPV can be effectively separated under weak turbulence conditions. Under the condition of limited available space and OAM states, the proposed DSDM strategy exploiting MRPV might inspire wide optical communication applications exploiting the space dimension of light beams.