you can still check “everything”. Because Icinga only triggers checks you’ve installed (Monitoring Plugins, NRPE, Icinga Powershell Framework etc.) and process the check result. You only need a check what is doing what you like to check…
So you can take a look into the typical sources like https://exchange.icinga.com/ or https://exchange.nagios.org/ if still sombody wrote a check or you write your own check in your preferred programming or scripting. language.