In the last decade, Approximate Computing (AxC) has been studied as a possible alternative computing paradigm. It has been used to reduce the overhead cost of conventional fault tolerant schemes, such as the Triple Modular Redundancy (TMR). One of the most recent propositions is the concept of Quadruple Approximate Modular Redundancy (QAMR). QAMR reduces the overhead cost w.r.t. conventional TMR structures, while guaranteeing the same fault-tolerance capability. In this paper, we propose a new approximation technique to realize the QAMR and we perform a Design Space Exploration (DSE) to find QAMR Pareto-optimal implementations. Moreover, we provide the design of a new majority voter for the proposed architecture. Experimental results show that it is possible to find QAMR variants achieving area and/or delay gains compared to the TMR counterpart, for 85.4% and 97% of the examined circuits for FPGA and ASIC technologies respectively.