This letter introduces a multi-rate task-oriented communication (MR-ToC) framework. This framework dynamically adapts to variations in affordable data rate within the communication pipeline. It conceptualizes communication pipelines as symmetric, discrete, memoryless channels. We employ a progressive learning strategy to train the system, comprising a nested codebook for encoding and task inference. This configuration allows for the adjustment of multiple rate levels in response to evolving channel conditions. The results from our experiments show that this system not only supports edge inference across various coding levels but also excels in adapting to variable communication environments.