With pip there isn't a concept of 'newest stable' as there is in Debian/Ubuntu.
The 'newest stable' packages in Debian/Ubuntu are tested to work correctly with all the other packages in the distribution.
With pip, you can upgrade all the python modules, but you will upgrade all the modules to the latest version available in the repository. It will be your responsibility to verify that everything still continues to work. There may be issues due to new bugs or incompatible changes.
Because of that never upgrade the OS provided python modules with pip (option: --system) unless you're ready to repair the possible breakage.
It can make a lot of sense to upgrade all the modules installed in your user environment, or better inside a virtual environment. The command should be:
pip freeze | awk '{print $1}' | xargs pip install -U
For users of different distributions and other cases, check:
pip help install
since the default behavior (no --user or --system options) changes from Debian derivatives to standard python.