Previous work on the competitive retrieval setting focused on a single-query setting: document authors manipulate their documents so as to improve their future ranking for a given query. We study a competitive setting where authors opt to improve their document's ranking for multiple queries. We use game theoretic analysis to prove that equilibrium does not necessarily exist. We then empirically show that it is more difficult for authors to improve their documents' rankings for multiple queries with a neural ranker than with a state-of-the-art feature-based ranker. We also present an effective approach for predicting the document most highly ranked in the next induced ranking.