Preserving the linguistic content of input speech is essential during voice conversion (VC). The star generative adversarial network-based VC method (StarGAN-VC) is a recently developed method that allows non-parallel many-to-many VC. Although this method is powerful, it can fail to preserve the linguistic content of input speech when the number of available training samples is extremely small. To overcome this problem, we propose the use of automatic speech recognition to assist model training, to improve StarGAN-VC, especially in low-resource scenarios. Experimental results show that using our proposed method, StarGAN-VC can retain more linguistic information than vanilla StarGAN-VC.