Current per-shot encoding schemes aim to improve the compression efficiency by shot-level optimization. It splits a source video sequence into shots and imposes optimal sets of encoding parameters to each shot. Per-shot encoding achieved approximately 20% bitrate savings over baseline fixed QP encoding at the expense of pre-processing complexity. However, the adjustable parameter space of the current per-shot encoding schemes only has spatial resolution and QP/CRF, resulting in a lack of encoding flexibility. In this paper, we extend the per-shot encoding framework in the complexity dimension. We believe that per-shot encoding with flexible complexity will help in deploying user-generated content. We propose a rate-distortion-complexity optimization process for encoders and a methodology to determine the coding parameters under the constraints of complexities and bitrate ladders. Experimental results show that our proposed method achieves complexity constraints ranging from 100% to 3% in a dense form compared to the slowest per-shot anchor. With similar complexities of the per-shot scheme fixed in specific presets, our proposed method achieves BDrate gain up to -19.17%.