You can re-mount your volume from inside the container, in the rw mode, like that:

mount -o remount,rw /mnt/data

The catch is that mount syscall is not allowed inside the Docker containers by default so that you would have to run it in a privileged mode:

docker run --privileged ...

or enable the SYS_ADMIN capability

SYS_ADMIN Perform a range of system administration operations.

docker run --cap-add=SYS_ADMIN --security-opt apparmor:unconfined

(note that I have had to also add --security-opt apparmor:unconfined, to make this work on Ubuntu).

Also, remounting the rw volume back to ro might be tricky, as some process(es) might have already opened some files inside it for writing , in which case the remount will fail with is busy error message.

But my guess is that you can just restart the container instead (as it would be the one running an old version of the app).

Not exactly what the OP requested, but I've had a similar question where i needed to get data OUT of the running container, but had mounted RW.

Other ways to extract the data would have taken too long.

My approach ? Stash the container as an image and start a new container from that Image with a mount as RW :D

Initial container start:

docker run  -p 80:8080 --mount type=bind,source="C:\data-folder-local\",target=/data-folder-container-ro,readonly -d imageName:imageTag

Making an image from the container. You can stop this container before/after if you want.

docker commit -a "mud" -m "Damn, mount should be rw, stashing a snapshot to reuse." CONTAINER_ID_HERE snapshotImageName:snapshotImageTag

where CONTAINER_ID_HERE i got from the output of docker ps (https://docs.docker.com/engine/reference/commandline/ps/)

Start a new container from the image made, but this time mount with write rights!

docker run  -p 80:8080 --mount type=bind,source="C:\data-folder-local\",target=/data-folder-container-rw -d snapshotImageName:snapshotImageTag

write out files to the mount folder (on local system) from within your container :D

Hope that helps somebody.