Spintronics-based synthetic neural networks (ANNs) exhibiting nonvolatile, quick, and energy-efficient computing capabilities are promising neuromorphic {hardware} for performing complicated cognitive duties of synthetic intelligence and machine studying. Early experimental efforts centered on multistate machine ideas to boost synaptic weight precisions, albeit compromising on cognitive accuracy attributable to their low magnetoresistance. Right here, we suggest a hybrid strategy based mostly on the tuning of tunnel magnetoresistance (TMR) and the variety of states within the compound magnetic tunnel junctions (MTJs) to enhance the cognitive efficiency of an all-spin ANN. A TMR variation of 33–78% is managed by the free layer (FL) thickness wedge (1.6–2.6 nm) throughout the wafer. In the meantime, the variety of resistance states within the compound MTJ is manipulated by various the variety of constituent MTJ cells (n = 1–3), producing n + 1 states with a TMR distinction between consecutive states of not less than 21%. Utilizing MNIST handwritten digit and style object databases, the take a look at accuracy of the compound MTJ ANN is noticed to extend with the variety of intermediate states for a set FL thickness or TMR. In the meantime, the take a look at accuracy for a 1-cell MTJ will increase linearly by 8.3% and seven.4% for handwritten digits and style objects, respectively, with growing TMR. Curiously, a multifarious TMR dependence of take a look at accuracy is noticed with the growing synaptic complexity within the 2- and 3-cell MTJs. By leveraging on the bimodal tuning of multilevel and TMR, we set up viable paths for enhancing the cognitive efficiency of spintronic ANN for in-memory and neuromorphic computing.