Style is an integral component of text that expresses a diverse set of information, including interpersonal dynamics (e.g. formality) and the author's emotions or attitudes (e.g. disgust). Humans often employ multiple styles simultaneously. An open question is how large language models can be explicitly controlled so that they weave together target styles when generating text: for example, to produce text that is both negative and non-toxic. Previous work investigates the controlled generation of a single style, or else controlled generation of a style and other attributes. In this paper, we expand this into controlling multiple styles simultaneously. Specifically, we investigate various formulations of multiple style rewards for a reinforcement learning (RL) approach to controlled multi-style generation. These reward formulations include calibrated outputs from discriminators and dynamic weighting by discriminator gradient magnitudes. We find that dynamic weighting generally outperforms static weighting approaches, and we explore its effectiveness in 2- and 3-style control, even compared to strong baselines like plug-and-play model. All code and data for RL pipelines with multiple style attributes will be publicly available.