Agentic LLM workflows issue many dependent calls with unpredictable resource demand, causing queue buildup and latency degradation on shared serving backends when left unmanaged. In this paper, we propose CALM-MAS, a congestion-aware serving framework for LLM applications that treats LLM test-time computation as an elastic resource, dynamically adjusting the compute profile of admitted tasks to tame congestion. CALM-MAS detects early signals of backend saturation, and leverages the flexibility of LLM applications to regulate load. During spikes of requests, the system downgrades agent topology and reasoning depth; during low-utilization periods, it allocates additional reasoning effort to maximize task accuracy. Compared with a static serving baseline based on vLLM, CALM-MAS reduces shared-backend tail latency by 77% with the accuracy degradation remaining confined to 6.1 pps relative to the native agent configuration.