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Motivated by the recent concept of Space-Time Shift Keying (STSK), we propose a novel cooperative STSK family, which is capable of achieving a flexible rate-diversity tradeoff, in the context of cooperative space-time transmissions. More specifically, we first propose a Coherent cooperative STSK (CSTSK) scheme, where each Relay Node (RN) activates Decode and-Forward (DF) transmissions, depending on the success or failure of Cyclic Redundancy Checking (CRC). We invoke a bit to-STSK mapping rule, where according to the input bits, one of the Q pre-assigned dispersion vectors is activated to implicitly convey log2 Q bits, which are transmitted in combination with the classic log2 L-bit modulated symbol. Additionally, we introduce a beneficial dispersion vector design, which enables us to dispense with symbol-level Inter-Relay Synchronization (IRS). Further more, the Destination Node (DN) is capable of jointly detecting the signals received from the source-destination and relay destination links, using a low-complexity single-stream-based Maximum Likelihood (ML) detector, which is an explicit benefit of our Inter-Element Interference (IEI)-free system model. More importantly, as a benefit of its design flexibility, our cooperative CSTSK arrangement enables us to adapt the number of the RNs, the transmission rate as well as the achievable diversity order. Moreover, we also propose a Differentially-encoded cooperative STSK (DSTSK) arrangement, which dispenses with CSI estimation at any of the nodes, while retaining the fundamental benefits of the cooperative CSTSK scheme.