REST APIs (Representational State Transfer Application Programming Interfaces) play a vital role in modern cloud-native applications. As these APIs grow in complexity and scale, ensuring their correctness and robustness becomes increasingly important. Automated testing is essential for identifying hidden bugs, particularly those that appear in edge cases or under unexpected inputs. However, creating comprehensive and effective test suites for REST APIs is challenging and often demands significant effort. In this paper, we investigate the use of large language model (LLM) systems, both single-agent and multi-agent setups, for amplifying existing REST API test suites. These systems generate additional test cases that aim to push the boundaries of the API, uncovering behaviors that might otherwise go untested. We present a comparative evaluation of the two approaches across several dimensions, including test coverage, bug detection effectiveness, and practical considerations such as computational cost and energy usage. Our evaluation demonstrates increased API coverage, identification of numerous bugs in the API under test, and insights into the computational cost and energy consumption of both approaches.