Generative adversarial networks (GANs) are showing significant promise for procedural content generation (PCG) of game levels. GAN models generate game levels by mapping a low dimensional latent space to game levels in the game space. An intriguing challenge in GAN-based PCG is enabling GANs to produce game levels for multiple distinct games with similar gameplay characteristics using a common underlying low-dimensional representation. In this paper, we present a method for training a novel GAN-based PCG architecture that generates levels in multiple distinct games, starting from a common gameplay action sequence. We evaluate the solvability of the generated games using an automated playing agent and show how the generated game levels are separate representations of the same gameplay by quantifying the similarity between the solution action sequences for the game levels. By probing the common latent space, we show how our approach provides control over the levels generated in distinct games for the presence of desired gameplay patterns in the generated game levels. Results also demonstrate that the GAN-based PCG approach creates novel game levels in multiple distinct games, as indicated by the distance between the action sequences required to solve the game levels.