Even though it’s “just” a compiler, GCC is tied to a number of core packages, which means it’s difficult to upgrade to a newer version than the version around which a Debian release is based (in Debian 11, that’s GCC 10). Ultimately you risk breaking your setup.

You could manually build GCC 11 on your Debian 11 system, but in practice it should be much easier to run your builds in a Debian 12 container (which will have GCC 11).

This is not recommended but you can install version 11.3 by downloading gcc-11 (version 11.3) from here. And downloading the dependencies gcc-11-base and libgcc-11-dev.

Then, run sudo apt install /path/to/file where /path/to/file is the path to the actual downloaded file. If it can't find the file, you may need to put it in double quotes like "/path/to/file".

You will need to install the gcc-11-base package first, then libgcc-11-dev and finally, gcc-11.

For example, if it's downloaded to your Downloads directory:

sudo apt install $HOME/Downloads/gcc-11-base_11.3.0-6ubuntu1_amd64.deb

and

sudo apt install $HOME/Downloads/libgcc-11-dev_11.3.0-6ubuntu1_amd64.deb

and

sudo apt install $HOME/Downloads/gcc-11_11.3.0-6ubuntu1_amd64.deb

I'm pretty sure gcc only requires gcc-11 >11.2 so this should downgrade your version of gcc and when you're done compiling or whatever you need it for, simply run:

sudo apt update
sudo apt install --reinstall gcc-11 gcc-11-base libgcc-11-dev

to upgrade back to the current version of gcc-11 (11.4).

Granted, the installation isn't guaranteed to work, could be insecure or lacking security updates. Also, you may run into dependency issues. If that's the case, you'd have to tread carefully or install each dependency one by one but always pay attention to what, if any, packages would need to uninstall when installing weird versions because you don't want to inadvertently uninstall a bunch of stuff you want or need.

EDIT: you will need to install dependencies (included above) but you can run the following commands to do it more quickly.

Run the following commands to create a working directory and download the packages:

cd
mkdir GCC11.3
cd GCC11.3
wget 'http://mirrors.kernel.org/ubuntu/pool/main/g/gcc-11/gcc-11-base_11.3.0-6ubuntu1_amd64.deb'
wget 'http://mirrors.kernel.org/ubuntu/pool/main/g/gcc-11/libgcc-11-dev_11.3.0-6ubuntu1_amd64.deb'
wget 'http://mirrors.kernel.org/ubuntu/pool/universe/g/gcc-11/gcc-11_11.3.0-6ubuntu1_amd64.deb'

Now, install the packages. Again, however, remember to pay attention to what, if any packages will be uninstalled when you install these weird versions. Review the list before you select Y to accept the changes!:

sudo apt install ./gcc*.deb

And again, when you're done compiling or whatever you need gcc 11.3 for, simply run:

sudo apt install --reinstall gcc-11 gcc-11-base libgcc-dev

to upgrade back to gcc 11.4.