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Despite significant advances in image-to-image (I2I) translation with generative adversarial networks (GANs), it remains challenging to effectively translate an image to a set of diverse images in multiple target domains using a single pair of generator and discriminator. Existing I2I translation methods adopt multiple domain-specific content encoders for different domains, where each domain-specific content encoder is trained with images from the same domain only. Nevertheless, we argue that the content (domain-invariance) features should be learned from images among all of the domains. Consequently, each domain-specific content encoder of existing schemes fails to extract the domain-invariant features efficiently. To address this issue, we present a flexible and general SoloGAN model for efficient multimodal I2I translation among multiple domains with unpaired data. In contrast to existing methods, the SoloGAN algorithm uses a single projection discriminator with an additional auxiliary classifier and shares the encoder and generator for all domains. Consequently, the SoloGAN can be trained effectively with images from all domains such that the domain-invariance content representation can be efficiently extracted. Qualitative and quantitative results over a wide range of datasets against several counterparts and variants of the SoloGAN demonstrate the merits of the method, especially for challenging I2I translation datasets, i.e., datasets involving extreme shape variations or need to keep the complex backgrounds unchanged after translations. Furthermore, we demonstrate the contribution of each component in SoloGAN by ablation studies.