I am on Linux Mint 20.3 Una. My environment contains already a pip, used by python3.8:

pip --version
pip 20.0.2 from /usr/lib/python3/dist-packages/pip (python 3.8)

python3 links to python3.8

ls -l /usr/bin/python3
/usr/bin/python3 -> python3.8

I have python3.9 installed. I want to install a pip/pip3 specific to python3.9.
It may install files in /usr/lib/python3.9/dist-packages/pip or pip3 or wherever it wants to, as long as both pip’s are fully compartmented.

Is it possible to do so?

I read answers on stackoverflow and similar websites to questions that are very close to mine, but the answers vary significantly : use repo deadsnakes, download pip-script.py, run python3.9 -m pip install pip.

Which solution is the best?

I did not try anything. I do not want to break my installation of python. Yesterday I installed python3.9 then set it as default, and today I had to revert python3 to python3.8 because my cinnamon was badly broken with python3.9 (no Terminal, no internet, no taskbar, no menu button), with all the panic inherent to seeing the machine becoming completely cripled.

I can still backup the folder

/usr/lib/python3/dist-packages/pip

Would it be enough of a safety net to revert any mistake made on pip?

It makes me feel like walking on eggs, with steel shoes.

I want to keep untouched the pip packages that are used by Linux Mint with python3.8.