How to increase volume above the system's maximum volume?

I'm afraid this is a issue on googles end and there is nothing you will be able to do as it is a problem within chrome/youtube itself and not your computer, I've experience the same thing with multiple OS's, always in chrome with youtube.

Install Ubuntu Linux (you can dual boot [aka. duel boot with Windows]), and then open gnome-terminal and do

sudo passwd
sudo su root

apt-get update
apt-get dist-upgrade
apt-get ubuntu-restricted-extras
apt-get install pavucontrol
exit

pavucontrol

And there you go ;)

pavucontrol: PulseAudio Volume Control

For Microsoft Windows:
See here for the pavucontrol-equivalent.