It is desirable to include more controllable attributes to enhance the diversity of generated responses in open-domain dialogue systems. However, existing methods can generate responses with only one controllable attribute or lack a flexible way to generate them with multiple controllable attributes. In this paper, we propose a Progressively trained Hierarchical Encoder-Decoder (PHED) to tackle this task. More specifically, PHED deploys Conditional Variational AutoEncoder (CVAE) on Transformer to include one aspect of attributes at one stage. A vital characteristic of the CVAE is to separate the latent variables at each stage into two types: a global variable capturing the common semantic features and a specific variable absorbing the attribute information at that stage. PHED then couples the CVAE latent variables with the Transformer encoder and is trained by minimizing a newly derived ELBO and controlled losses to produce the next stage's input and produce responses as required. Finally, we conduct extensive evaluations to show that PHED significantly outperforms the state-of-the-art neural generation models and produces more diverse responses as expected.