Neural Architecture Search has proven an effective method of automating\narchitecture engineering. Recent work in the field has been to look for\narchitectures subject to multiple objectives such as accuracy and latency to\nefficiently deploy them on different target hardware. Once-for-All (OFA) is one\nsuch method that decouples training and search and is able to find\nhigh-performance networks for different latency constraints. However, the\nsearch phase is inefficient at incorporating multiple latency targets. In this\npaper, we introduce two strategies (Top-down and Bottom-up) that use warm\nstarting and randomized network pruning for the efficient incorporation of\nmultiple latency targets in the OFA network. We evaluate these strategies\nagainst the current OFA implementation and demonstrate that our strategies\noffer significant running time performance gains while not sacrificing the\naccuracy of the subnetworks that were found for each latency target. We further\ndemonstrate that these performance gains are generalized to every design space\nused by the OFA network.\n