Create cloud optimized GeoTIFF without re-encoding?

I have a lot of jpeg-in-geotiff imagery that I would like to convert to Cloud Optimized GeoTIFF. Is there any way to do that without re-encoding the pixel values?

I’m trying to avoid paying the price of:

• lossy + lossy compression that results from feeding a JPEG source to a JPEG output file, and
• lossy + lossless that comes from feeding a JPEG source to lossless output file, which means x4+ storage requirements