Deep learning is increasingly impacting various aspects of contemporary society. Artificial neural networks have emerged as the dominant models for solving an expanding range of tasks. The introduction of Neural Architecture Search (NAS) techniques, which enable the automatic design of task-optimal networks, has led to remarkable advances. However, the NAS process is typically associated with long execution times and significant computational resource requirements. Once-For-All (OFA) and its successor, Once-For-All-2 (OFAv2), have been developed to mitigate these challenges. While maintaining exceptional performance and eliminating the need for retraining, they aim to build a single super-network model capable of directly extracting sub-networks satisfying different constraints. Neural Architecture Transfer (NAT) was developed to maximise the effectiveness of extracting sub-networks from a super-network. In this paper, we present NATv2, an extension of NAT that improves multi-objective search algorithms applied to dynamic super-network architectures. NATv2 achieves qualitative improvements in the extractable sub-networks by exploiting the improved super-networks generated by OFAv2 and incorporating new policies for initialisation, pre-processing and updating its networks archive. In addition, a post-processing pipeline based on fine-tuning is introduced. Experimental results show that NATv2 successfully improves NAT and is highly recommended for investigating high-performance architectures with a minimal number of parameters.