Several recent works have demonstrated the use of variational autoencoders (VAEs) for both generating levels in the style of existing games as well as blending levels across different games. Additionally, quality-diversity (QD) algorithms have also become popular for generating varied game content by using evolution to explore a search space while focusing on both variety and quality. In order to reap the benefits of both these approaches, we present a level generation and game blending approach that combines the use of VAEs and QD algorithms. Specifically, we train VAEs on game levels and then run the MAP-Elites QD algorithm using the learned latent space of the VAE as the search space. The latent space captures the properties of the games whose levels we want to generate and blend, while MAP-Elites searches this latent space to find a diverse set of levels optimizing a given objective such as playability. We test our method using models for 5 different platformer games as well as a blended domain spanning 3 of these games. Our results show that using MAP-Elites in conjunction with VAEs enables the generation of a diverse set of playable levels not just for each individual game but also for the blended domain while illuminating game-specific regions of the blended latent space.