Comment by trhway

doesn't scale well. The amount of air entering is proportional to square - cross-section - while the mass of rocket is cubic. While scramjet/turbojet/air-augmentation, say as a separate detachable stage, can be pretty efficient for smaller rocket, anything making significant improvement for say Starship would looks like a fat monster cross-section-wise with tremendous hardware cost and weight loosing outright to the straight option of adding additional tanks and rocket engines.

Wrt. aerospike engine - sounds nice, yet hardware wise it is heavier than the classic engine, and just look at that large number of pieces - just all those small mini-engines - it is made of and compare to Raptor 3. And for the optimal expansion - i'm waiting somebody will add a dynamically adjusting telescopic kind of end section to the classic bell nozzle.

A napkin to illustrate. Lets say you add a Raptor and 80 tons of fuel plus oxygen for it. That will give you 100 seconds of excess impulse of at least 160 tons (240 ton of thrust minus 80 tons) at the beginning to 240 tons at the end, so roughly 100 seconds of 200 tons. To get 200 tons thrust you'd need 20 fighter turbojet engines capable of at least Mach 3 - that is cost, complexity and weight dwarfing that one Raptor engine.

For scramjet, assuming we got a decent one, napkin is about the same. The best, my favorite, is air-augmented - scram-compress the air and channel it on the outside of the hot bell nozzles of the already working rocket engines - unfortunately the scaling mentioned above comes into play for meaningfully sized rockets though it has worked great for small ones.