This paper proposes a novel relay-aided intelligent reconfigurable surface (IRS) architecture for future wireless communication systems. The proposed architecture, which consists of two side-by-side intelligent surfaces connected via a full-duplex relay, has the potential of achieving the promising gains of intelligent surfaces while requiring much smaller numbers of reflecting elements. Consequently, the proposed IRS architecture needs significantly less channel estimation and beam training overhead and provides higher robustness compared to classical IRS approaches. Further, thanks to dividing the IRS reflection process over two surfaces, the position and orientation of these surfaces can be optimized to extend the wireless communication coverage and enhance the system performance. In this paper, the achievable rates and required numbers of elements using the proposed relay-aided IRS architecture are first analytically characterized and then evaluated using numerical simulations. The results show that the proposed architecture can achieve the data rate targets with much smaller numbers of elements compared to typical IRS solutions, which highlights a promising path towards the practical deployment of these intelligent surfaces.