This paper investigates simultaneous modeling of multiple emotions in DNN-based expressive speech synthesis, and how to represent the emotional labels, such as emotional class and strength, for this task. Our goal is to answer two questions: First, what is the best way to annotate speech data with multiple emotions? Second, how should the emotional information be represented as labels for supervised DNN training? We evaluate on a large-scale corpus of emotional speech from a professional actress, additionally annotated with perceived emotional labels from crowd-sourced listeners. By comparing DNN-based speech synthesizers that utilize different emotional representations, we assess the impact of these representations and design decisions on human emotion recognition rates.