Adaptive video streaming systems typically support different media delivery formats, e.g., MPEG-DASH and HLS, replicating the same content multiple times into the network. Such a diversified system results in inefficient use of storage, caching, and bandwidth resources. The Common Media Application Format (CMAF) emerges to simplify HTTP Adaptive Streaming (HAS), providing a single encoding and packaging format of segmented media content and offering the opportunities of bandwidth savings, more cache hits and less storage needed. However, CMAF is not yet supported by most devices. To solve this issue, we present a solution where we maintain the main advantages of CMAF while supporting heterogeneous devices using different media delivery formats. For that purpose, we propose to dynamically convert the content from CMAF to the desired media delivery format at an edge node. We study the bandwidth savings with our proposed approach using an analytical model and simulation, resulting in bandwidth savings of up to 20% with different media delivery format distributions. We analyze the runtime impact of the required operations on the segmented content performed in two scenarios: the classic one, with four different media delivery formats, and the proposed scenario, using CMAF-only delivery through the network. We compare both scenarios with different edge compute power assumptions. Finally, we perform experiments in a real video streaming testbed delivering MPEG-DASH using CMAF content to serve a DASH and an HLS client, performing the media conversion for the latter one.