Weight-sharing neural architecture search aims to optimize a configurable neural network model (supernet) for a variety of deployment scenarios across many devices with different resource constraints. Existing approaches use evolutionary search to extract models of different sizes from a supernet trained on a very large data set, and then fine-tune the extracted models on the typically small, real-world data set of interest. The computational cost of training thus grows linearly with the number of different model deployment scenarios. Hence, we propose Transfer-Once-For-All (TOFA) for supernet-style training on small data sets with constant computational training cost over any number of edge deployment scenarios. Given a task, TOFA obtains custom neural networks, both the topology and the weights, optimized for any number of edge deployment scenarios. To overcome the challenges arising from small data, TOFA utilizes a unified semi-supervised training loss to simultaneously train all subnets within the supernet, coupled with on-the-fly architecture selection at deployment time.