While I was thinking of possible researches on the moons of Jupiter and Saturn, I realized that there weren't many satellites operating at such long distances. I thought that lowering the cost of such missions would increase their number.
I thought about a two staged rocket. The first stage will only lift the rocket vertically up to the Kármán line. The second stage of the rocket will also be staged, but with a much radical design. The propellent tanks will be grouped by two (oxidizer + fuel). They will be connected to the engine of the rocket via external piping. There will be junctions on the tank connections. These junctions will control the flow and turn on and off the connections. There will be four pipes; first one for the propellent, second one for the oxidizer and the last two for the exhaust gas used to pressurize the tanks. Each tank will have a thin film separating the propellent from the exhaust gas. This film will eliminate direct contact of the exhaust and the propellent. Additionally, eliminate the sloshing inside the tank. The exhaust gas will be cooled to adequate temperatures inside the engine bay before released to the tanks.
Once a group of tanks are depleted, the junction box will disconnect them from the main pipes and the next group will be connected. Then, the upper section of the junction box and other attachment points will be ignited to release the empty tanks. Slightly tilted design of the tanks will also help. After the empty tank pipe connections are broken, the pressurizing gas inside will escape and push the tanks away from the rocket.
As a result, the upper stage will only have one vacuum optimized nozzle and one engine. Whereas rockets with more stages need to have as many of these as the number of stages. This saves weight and extends the range of the rocket. The huge nozzle will be designed to accommodate room for the payload of the rocket.
Vacuum only operation of this stage and slow speed through the atmosphere would allow such design.