Short answer, you can’t do it from the basic settings from the admin.
However, you can do a trick that will do exactly what you want.
Let’s say you want to have two flat rates for shipping, one for cities and one for rural areas.
You can set the default “flat rate” method.
And also enable the shipping method called “shipping by weight”.
From “Shipping by weight”, select to enable it, pick the country where you are selling, and set at “rate” something like “9999:40”.
This means for at least 99999 kg, the shipping fee is 40 (dollars or euro, or whatever currency your store is using).
After that, you want to modify the language (the text that will appear when the customer has clicked to calculate the shipping fees).
Go to “catalog” > “languages” > “english” > “shipping” > weight.php and change the text into what you want.
If you don’t manage, use a find and replace program like Notepad++ to find the text that you want replaced.
Note that instead of an English folder, you might have another one with your current language that the store is using.
This way, the customer will see two shipping fees, the one called flat rate and the second one that you can name it as you want from languages (it will be taken from the shipping by weight shipping method).
If you have any questions, leave in the comments.