Proof-of-Space provides an intriguing alternative for consensus protocol of permissionless blockchains due to its recyclable nature and the potential to support multiple chains simultaneously. However, a direct shared proof of the same storage, which was adopted in the existing multi-chain schemes based on Proof-of-Space, could give rise to newborn attack on new chain launching. To fix this gap, we propose an innovative framework of single-chain Proof-of-Space and further present a novel multi-chain scheme which can resist newborn attack effectively by elaborately combining shared proof and chain-specific proof of storage. Moreover, we analyze the security of the multi-chain scheme and prove that it is incentive-compatible. This means that participants in such multi-chain system can achieve their greatest utility with our proposed strategy of storage resource partition.