Spiking neural P systems (SNP systems) are parallel and non-deterministic models of computation, inspired by the neural system of the brain. A variant of SNP systems known as SNP systems with structural plasticity (SNPSP systems) includes the feature of adding or removing synapses among neurons. This feature is inspired by plasticity from neuroscience during cognition and learning. Despite the reductionist framework of SNP and SNPSP systems, such as brain-like systems are capable of computational universality. In particular, we use SNPSP systems in this paper to compute some classes of languages from the Chomsky hierarchy: FIN, REG, and RE. The computations of such classes continue a research direction established in the previous paper. We also emphasize the (dis)advantages of synapse plasticity in the neural system, compared with existing features of SNP systems, when generating languages.