The JPEG file format is pretty detailed, there are lots of places in the file where you could indicate that the image has been compressed with a different algorithm. But it wouldn't really help, because older decompressors will still not be able to interpret the new codec. They would be able to parse the file and read the metadata in it - like image width and height, timestamps, camera details, and so on, but there's no way it can decompress the data.

PNG is a very nice, extensible container format. In principle you can use it to store arbitrary image data, and still make use of all established metadata fields.

In practice you probably shouldn't do that without changing the file extension and the magic bytes to avoid confusion among users and poorly written software.