The compound parabolic concentrator (CPC) is a core technology in the field of solar concentration. Nevertheless, it only has one degree of freedom in the choice of its half-acceptance angle. In this study, extending the idea of the three-dimensional CPC, a design method for new kinds of concentrators having a CPC shape at each profile with various acceptance angles in all directions is proposed. The feature of this method is that the receiver can take any shape. Here, elliptical and rectangular receivers are assumed, and the shape and concentration performance of the concentrators with multiple CPC profiles and an elliptical receiver (MultiPro-ECPCs) and the concentrators with multiple CPC profiles and a rectangular receiver (MultiPro-RCPCs) are derived. The new designs are compared to the conventional CPC and a mirrorless flat receiver through ray-tracing simulations in terms of energy distribution on the receiver, optical efficiency, and optical concentration ratio based on axial and solar angles. The results show that in terms of optical efficiency, the MultiPro-RCPCs cover a wider range of incident angles after the 3DCPC. In terms of the optical concentration ratio, the MultiPro-ECPC with a longitudinal half-acceptance angle of 15° has the highest peak value of 19.5, followed by the MultiPro-RCPC. This study enlightens that with the concentration system settings adapted to the acceptance range of the proposed concentrators, a higher concentration can be achieved with the MultiPro-ECPC and MultiPro-RCPC compared to the conventional CPC.