sudo apt install build-essential manpages-dev software-properties-common
sudo add-apt-repository ppa:ubuntu-toolchain-r/test
sudo apt update && sudo apt install gcc-11 g++-11

Then use update-alternatives to set default gcc...

sudo update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-9 90 --slave /usr/bin/g++ g++ /usr/bin/g++-9 --slave /usr/bin/gcov gcov /usr/bin/gcov-9 --slave /usr/bin/gcc-ar gcc-ar /usr/bin/gcc-ar-9 --slave /usr/bin/gcc-ranlib gcc-ranlib /usr/bin/gcc-ranlib-9  --slave /usr/bin/cpp cpp /usr/bin/cpp-9 && \

sudo update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-11 110 --slave /usr/bin/g++ g++ /usr/bin/g++-11 --slave /usr/bin/gcov gcov /usr/bin/gcov-11 --slave /usr/bin/gcc-ar gcc-ar /usr/bin/gcc-ar-11 --slave /usr/bin/gcc-ranlib gcc-ranlib /usr/bin/gcc-ranlib-11  --slave /usr/bin/cpp cpp /usr/bin/cpp-11;

To sample check settings to see which gcc is default you can run the following, if they show correct resuslts then the rest are fine...

gcc --version;g++ --version;gcov --version;

To reconfigure to any previous gcc version...

sudo update-alternatives --config gcc

You can do this on any version of ubuntu,... enjoy!

Here are my 6 different gcc's living side by side with the default being gcc-11:

$ sudo update-alternatives --config gcc
There are 6 choices for the alternative gcc (providing /usr/bin/gcc).

  Selection    Path             Priority   Status
------------------------------------------------------------
* 0            /usr/bin/gcc-11   1010      auto mode
  1            /usr/bin/gcc-10   1000      manual mode
  2            /usr/bin/gcc-11   1010      manual mode
  3            /usr/bin/gcc-5    40        manual mode
  4            /usr/bin/gcc-7    700       manual mode
  5            /usr/bin/gcc-8    800       manual mode
  6            /usr/bin/gcc-9    900       manual mode

Press <enter> to keep the current choice[*], or type selection number:

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.