RISE AB RISE AB Object Security for Constrained RESTful Environments (OSCORE) can be used to protect CoAP messages end-to-end between two endpoints at the application layer, also in the presence of intermediaries such as proxies. This document defines how to use OSCORE for protecting CoAP messages also between an origin application endpoint and an intermediary, or between two intermediaries. Also, it defines rules to escalate the protection of a CoAP option, in order to encrypt and integrity-protect it whenever possible. Finally, it defines how to secure a CoAP message by applying multiple, nested OSCORE protections, e.g., both end-to-end between origin application endpoints, and between an application endpoint and an intermediary or between two intermediaries. Therefore, this document updates RFC 8613. Furthermore, this document updates RFC 8768, by explicitly defining the processing with OSCORE for the CoAP option Hop-Limit. The approach defined in this document can be seamlessly used with Group OSCORE, for protecting CoAP messages when group communication is used in the presence of intermediaries.