a server just for asp capability

Are there any services out there that just offer asp capabilities?
I've been using this basic webserver which is real cheap, but pretty much only has client side abilities. I'd like to move up and integrate some basic databases and asp, but love the service i'm using and don't want to change.

They do offer upgraded plans with asp , but its beyond my price range. So I was wondering if I have the option of hosting my website one place and asp/databases from another server. Is this even possible?