Biomedical entity linking models disambiguate mentions in text by matching them with unique biomedical concepts. This problem is commonly addressed using a two-stage pipeline comprising an inexpensive candidate generator, which filters a subset of suitable entities for a mention, and a costly but precise reranker that provides the final matching between the mention and the concept. With the goal of applying two-stage entity linking at scale, we explore the construction of effective cross-encoder reranker models, capable of scoring multiple mention-entity pairs simultaneously. Through experiments on four entity linking datasets, we show that our cross-encoder models provide between 2.7 to 36.97 times faster training speeds and 3.42 to 26.47 times faster inference speeds than a base cross-encoder model capable of scoring only one entity, while achieving similar accuracy (differences between -3.42% to 2.76% Acc@1).