Modern Generative Adversarial Networks (GANs) generate realistic images remarkably well. Previous work has demonstrated the feasibility of “GAN-classifiers” that are distinct from the co-trained discriminator, and operate on images generated from a frozen GAN. That such classifiers work at all affirms the existence of “knowledge gaps” (out-of-distribution artifacts across samples) present in GAN training. We iteratively train GAN-classifiers and train GANs that “fool” the classifiers (in an attempt to fill the knowledge gaps), and examine the effect on GAN training dynamics, output quality, and GAN-classifier generalization. We investigate two settings, a small DCGAN architecture trained on low dimensional images (MNIST), and StyleGAN2, a SOTA GAN architecture trained on high dimensional images (FFHQ). We find that the DCGAN is unable to effectively fool a held-out GAN-classifier without compromising the output quality. However, StyleGAN2 can fool held-out classifiers with no change in output quality, and this effect persists over multiple rounds of GAN/classifier training which appears to reveal an ordering over optima in the generator parameter space. Finally, we study different classifier architectures and show that the architecture of the GAN-classifier has a strong influence on the set of its learned artifacts.