Most blockchain-based cryptocurrencies suffer from a heavily limited transaction throughput, which is a barrier to their growing adoption. Payment channel networks (PCNs) are one of the promising solutions to this problem. PCNs reduce the on-chain load of transactions and increase the throughput by processing many payments off-chain. In fact, any two users connected via a path of payment channels (i.e., joint addresses between the two channel end-points) can perform payments, and the underlying blockchain is used only when there is a dispute between users. Unfortunately, payments in PCNs can only be conducted securely along a path, which prevents the design of many interesting applications. Moreover, the most widely used implementation, the Lightning Network in Bitcoin, suffers from a collateral lock time linear in the path length, it is affected by security issues, and it relies on specific scripting features called Hash Timelock Contracts that hinders the applicability of the underlying protocol in other blockchains. In this work, we present Thora, the first Bitcoin-compatible off-chain protocol that enables the atomic update of arbitrary channels (i.e., not necessarily forming a path). This enables the design of a number of new off-chain applications, such as payments across different PCNs sharing the same blockchain, secure and trustless crowdfunding, and channel rebalancing. Our construction requires no specific scripting functionalities other than digital signatures and timelocks, thereby being applicable to a wider range of blockchains. We formally define security and privacy in the Universal Composability framework and show that our cryptographic protocol is a realization thereof. In our performance evaluation, we show that our construction requires only constant collateral, independently from the number of channels, and has only a moderate off-chain communication as well as computation overhead.