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End-to-end (E2E) task-oriented dialogue (ToD) systems are prone to fall into the so-called "likelihood trap", resulting in generated responses which are dull, repetitive, and often inconsistent with dialogue history. Comparing ranked lists of multiple generated responses against the "gold response" (from evaluation data) reveals a wide diversity in response quality, with many good responses placed lower in the ranked list. The main challenge, addressed in this work, is then how to reach beyond greedily generated system responses, that is, how to obtain and select such high-quality responses from the list of overgenerated responses at inference without availability of the gold response. To this end, we propose a simple yet effective reranking method which aims to select high-quality items from the lists of responses initially overgenerated by the system. The idea is to use any sequence-level (similarity) scoring function to divide the semantic space of responses into high-scoring versus low-scoring partitions. At training, the high-scoring partition comprises all generated responses whose similarity to the gold response is higher than the similarity of the greedy response to the gold response. At inference, the aim is to estimate the probability that each overgenerated response belongs to the high-scoring partition, given only previous dialogue history. We validate the robustness and versatility of our proposed method on the standard MultiWOZ dataset: our methods improve a state-of-the-art E2E ToD system by 2.0 BLEU, 1.6 ROUGE, and 1.3 METEOR scores, achieving new peak results. Additional experiments on the BiTOD dataset and human evaluation further ascertain the generalisability and effectiveness of the proposed framework.