I have several images (3rd parties) which eg setup a mysql, set up a generic php app environment, set up 3rd parties tools.
I want to make a Dockerfile / Docker Image which combines both those images and then runs some more commands
imageA --
\
imageV -- ---> sharedImageA..X
/
imageX --
You can chain them. You can find more here
https://github.com/docker/docker/issues/3378#issuecomment-31314906
Taken from the above link
author of the above SvenDowideit
In general though, it's a bad practice to have more than one running processes on the same container.
Since dependencies from seconds and third image can conflict with dependencies from first image, I don't think docker would able to support it.
I guess the only option is to start your image from 1 of them an then install/run all of the steps from 2 others: