Neural Architecture Search (NAS) for deep learning object detection frameworks typically involves multiple modules, each performing distinct tasks. These modules contribute to a vast search space, resulting in searches that can take several GPU hours or even days, depending on the complexity of the search space. This makes joint optimization both challenging and computationally expensive. Furthermore, satisfying target device constraints across modules adds additional complexity to the optimization process. To address these challenges, we propose \textbf{FACETS}, e\textbf{\underline{F}}ficient Once-for-\textbf{\underline{A}}ll Object Detection via \textbf{\underline{C}}onstrained it\textbf{\underline{E}}ra\textbf{\underline{T}}ive\textbf{\underline{S}}earch, a novel unified iterative NAS method that refines the architecture of all modules in a cyclical manner. FACETS leverages feedback from previous iterations, alternating between fixing one module's architecture and optimizing the others. This approach reduces the overall search space while preserving interdependencies among modules and incorporates constraints based on the target device's computational budget. In a controlled comparison against progressive and single-module search strategies, FACETS achieves architectures with up to $4.75\%$ higher accuracy twice as fast as progressive search strategies in earlier stages, while still being able to achieve a global optimum. Moreover, FACETS demonstrates the ability to iteratively refine the search space, producing better performing architectures over time. The refined search space yields candidates with a mean accuracy up to $27\%$ higher than global search and $5\%$ higher than progressive search methods via random sampling.