Pre-trained Transformer-based large models have revolutionized personal virtual assistants, but their deployment in cloud environments faces challenges related to data privacy and response latency. Deploying large models closer to the data and users has become a key research area to address these issues. However, applying these models directly often entails significant difficulties, such as model mismatching, resource constraints, and energy inefficiency. Automated design of customized models is necessary, but it faces three key challenges, namely, the high cost of centralized model customization, imbalanced performance from user heterogeneity, and suboptimal performance from data heterogeneity. In this paper, we propose ACME, an adaptive customization approach of Transformer-based large models via distributed systems. To avoid the low cost-efficiency of centralized methods, ACME employs a bidirectional single-loop distributed system to progressively achieve fine-grained collaborative model customization. In order to better match user heterogeneity, it begins by customizing the backbone generation and identifying the Pareto Front under model size constraints to ensure optimal resource utilization. Subsequently, it performs header generation and refines the model using data distribution-based personalized architecture aggregation to match data heterogeneity. Evaluation on different datasets shows that ACME achieves cost-efficient models under model size constraints. Compared to centralized systems, data transmission volume is reduced to 6 percent. Additionally, the average accuracy improves by 10 percent compared to the baseline, with the trade-off metrics increasing by nearly 30 percent.