I am no longer a Dish customer, but they used to have a "Dual Tuner" receiver that allowed you to have 2 TV sets connected, with only one receiver and no extra charge. If they still have them, you could use 2 of those for your 4 TV sets.
They will probably charge you a lot for new equipment. I know many people, when faced with the cost of new receivers, cancelled Dish and called back later as a "New" customer. Of course, your 2-year commitment must be over or you will be forced to "buy out" your remaining months when you cancel.
As a Dish installer once said to me - "We give our NEW customers anything. But loyal customers, not so much."
A lot of people also connect only their main TV sets to the dish, and use a rooftop antenna for the other TV sets - in the kids room or the guest room, for example.
The only way I could think about to connect multiple Tvs is by using a splitter to literally split the receiver output cable into 2 or more different cables to go with the other TVs. The only problems is that depending on your receiver you may not be able to watch different channels at a time, your receiver may be able to only broadcast one for all TVs.
I have a DISH 722k with the optional OTA (Over The Air) module. I also have ran RG-6 coaxial cable at other rooms in the house. The 722k has several tuners and TV 1 and TV 2 output. The system is configured so that secondary sets can watch TV 1 or TV 2 content. As has already been pointed out, that doesn't allow totally independent viewing on all sets, however. My workaround is to also have digital to analog converter boxes on those sets. Since we are a family of four, it seems to work out pretty well for us. Typically my two sons will watch the same program on TV 2, if they are viewing Dish. Usually I will just watch whatever my wife selects. For those times that I want something else, I go to another room and make sure that my sons aren't watching something on TV 2 first. I also have extra UHF remote controls at each TV. We also have NetFlix and Hulu Plus, so often someone is watching that rather than Dish.
As a side note, several of my TVs are actually Samsung TVs that have PIP (Picture In Picture) feature. That allows us to look at the internet and have TV in the upper right corner of the TV monitor. Honestly, I am probably the only one in the family that uses that feature, but having the same device serve as a TV or computer monitor is handy for us.