Well Antony, the conditions are there exactly for this purpose. Add a condition for each group and it will be ignored if the condition is not met. So use the $_GET variable as a condition and it will be ignored if the GET variable returns no value ...
In my example if {{$_GET.country}} returns a value and {{$_GET.city}} does not - only the country filter will be applied. If {{$_GET.city}} also has a value, then country AND city will be applied.