Abstract-In this paper, we develop a capacity-approaching Cooperative Space-Time Coding (CSTC) scheme employing irregular design for a twin-relay aided network as an extension of our previous work cast in the context of a half-duplex singlerelay-aided network. For the sake of recovering the multiplexing loss imposed by a half-duplex three-terminal network, we employ a successive relaying protocol in this paper, where an additional relay node is activated. Hence, in order to design a near-capacity coding system, first the capacity and the achievable informationrate of a specific space-time coding aided scheme are quantified for the successive relaying aided channel. More specifically, the cooperative space-time codes employed at the source and the relays are jointly designed with the aid of EXtrinsic Information Transfer (EXIT) charts for the sake of high-integrity operation at Signal-to-Noise Ratios (SNRs) close to the corresponding successive relaying channel's capacity. Furthermore, unlike in the halfduplex single-relay based system, the destination node performs frame-by-frame Successive Interference Cancellation (SIC) aided iterative detection, in order to mitigate the efforts of multipleaccess interference. Finally, our numerical results demonstrate that our proposed Irregular Cooperative Space-Time Coding (Ir-CSTC) scheme is capable of near-capacity operation in the successive relaying aided network, which is an explicit benefit of our joint source-and-relay transceiver design.