This paper proposes a modification to RNN-Transducer (RNN-T) models for automatic speech recognition (ASR). In standard RNN-T, the emission of a blank symbol consumes exactly one input frame; in our proposed method, we introduce additional blank symbols, which consume two or more input frames when emitted. We refer to the added symbols as big blanks, and the method multi-blank RNN-T. For training multi-blank RNN-Ts, we propose a novel logit under-normalization method in order to prioritize emissions of big blanks.