Due to the continuously improving capabilities of mobile edges, recommender systems start to deploy models on edges to alleviate network congestion caused by frequent mobile requests. Several studies have leveraged the proximity of edge-side to real-time data, fine-tuning them to create edge-specific models. Despite their significant progress, these methods require substantial on-edge computational resources and frequent network transfers to keep the model up to date. The former may disrupt other processes on the edge to acquire computational resources, while the latter consumes network bandwidth, leading to a decrease in user satisfaction. In response to these challenges, we propose a customizeD slImming framework for incompatiblE neTworks(DIET). DIET deploys the same generic backbone (potentially incompatible for a specific edge) to all devices. To minimize frequent bandwidth usage and storage consumption in personalization, DIET tailors specific subnets for each edge based on its past interactions, learning to generate slimming subnets(diets) within incompatible networks for efficient transfer. It also takes the inter-layer relationships into account, empirically reducing inference time while obtaining more suitable diets. We further explore the repeated modules within networks and propose a more storage-efficient framework, DIETING, which utilizes a single layer of parameters to represent the entire network, achieving comparably excellent performance. The experiments across four state-of-the-art datasets and two widely used models demonstrate the superior accuracy in recommendation and efficiency in transmission and storage of our framework.