The starting position
SpaceX currently has the Falcon 9 we know well. The first version flew in 2010. It uses kerosene fuel with gas generator Merlin engines. The engine cycle is conservative and performance is fine. Falcon 9 has reusable components, the first stage lands back near the launch site or on a barge. Payload is 17 tons reusable and 23 t expendable.
SpaceX is developing the Starship. The Super Heavy first stage and Starship Spacecraft second stage. They are absolutely humongous. Super heavy has 33 and Starship six engines. They are made of stainless steel, welding on the spot at the Texas coastal site in Boca Chica. Both have had lots of development issues. Both use Raptor engines. Raptor is a very advanced staged combustion engine using methane fuel. Full flow staged combustion with extreme chamber pressures, leading to very high specific impulse and thrust to weight ratio.
SpaceX could start using Raptor (current version is Raptor-2) in a more straightforward rocket design instead of Super Heavy / Starship combo. What would it look like? I took the liberty of sketching what one would look like.
New launch vehicle (fictional)
Hawk 7 Double Falcon 9 payload First stage: Seven Raptor-2 engines Land with center engine only lit Second stage: One Raptor-2 engine with extendable-retractable vacuum nozzle extension Experimentally land with the engine lit, approaching ground at high speed and lighting late, because T/W>1. Payload fairing is kept attached to second stage. Same length as current Falcon 9, but wider.
This means all parts are reused.
Second stage can orbit the earth once and then land a few hundred km from the launch site.
Second stage can also land anywhere in the world near its orbital track, refuel (partially) and fly back to launch site. Hops might be short though, 300-600 km. It would be possible to build these stages anywhere, and if they are hard to transport, just fly them to the launch site.
Explanation – why this design?
The proven Falcon 9 propulsive landing technique requires a large difference in maximum takeoff and minimum landing thrust. Having 9 engines for takeoff and 1 for landing helps this. However, the Raptor 2 throttles more deeply than Merlin, hence a 7 to 1 ratio of takeoff to landing engines is enough. The minimum number is chosen to make the launcher as small as possible, to make it easy to build very soon. Also the least amount of ground equipment construction etc is needed. With 9 Raptors the launcher would become less practical and flexible.
Raptor has tremendous chamber pressure and thus great thrust density. It could support also a very tall rocket with small diameter if needed (like evidenced by Starship, a very tall rocket with still a lot of empty space at the base). The beauty about Raptor is that it would support whatever rocket shape would be operationally the easiest.
To keep launch facilities similar, similar length and larger diameter would be better. What if if it had same diameter as Falcon but was just longer, it could probably then utilize Falcon 9 tank and intertank manufacturing infrastructure? From load structure perspective a thicker rocket would probably be more optimal, Falcon 9 is already a very stretched design. If both stages can transport with suborbital hops, then transport infrastructure considerations (has to fit under bridges etc) that favor small diameter go away. It wouldn’t need to be nearly as wide as Starship at 9 meters. Robotic welding was used for Space Shuttle aluminum tanks with 8 meter diameter and the tanks were transported by barge from Michoud. Delta IV with 5 meter tanks is barged or shipped currently.
With the higher efficiency of the Raptor, these rockets should have more margin for total reusability. The lower coking from methane could potentially simplify reuse as well, lowering the time between flights of each stage.
What would it mean
If the second stage landing worked, total reusability would have the potential to lower the cost per kilogram to low earth orbit tremendously. If it fails, then, expending the second stage, the Hawk 7 dry rocket payload fraction should be a lot better than Falcon 9 and hence also dollars per payload kg.