Query expansion has been widely used to improve the search results of first-stage retrievers, yet its influence on second-stage, cross-encoder rankers remains under-explored. A recent work of Weller et al. [44] shows that current expansion techniques benefit weaker models such as DPR and BM25 but harm stronger rankers such as MonoT5. In this paper, we re-examine this conclusion and raise the following question: Can query expansion improve generalization of strong cross-encoder rankers? To answer this question, we first apply popular query expansion methods to state-of-the-art cross-encoder rankers and verify the deteriorated zero-shot performance. We identify two vital steps for cross-encoders in the experiment: high-quality keyword generation and minimal-disruptive query modification. We show that it is possible to improve the generalization of a strong neural ranker, by prompt engineering and aggregating the ranking results of each expanded query via fusion. Specifically, we first call an instruction-following language model to generate keywords through a reasoning chain. Leveraging self-consistency and reciprocal rank weighting, we further combine the ranking results of each expanded query dynamically. Experiments on BEIR and TREC Deep Learning 2019/2020 show that the nDCG@10 scores of both MonoT5 and RankT5 following these steps are improved, which points out a direction for applying query expansion to strong cross-encoder rankers.