So far nothing could beat just increasing the size of the first stage. Simplicity and weight as any air breathing hardware brings in weight and complexity. Even

So far nothing could beat just increasing the size of the first stage. Simplicity and weight as any air breathing hardware brings in weight and complexity. Even the simplest and my favorite approach - air augmentation - could not be made so far (beside a small USSR surface-to-air missile). Also with the size of the rocket the proportional air breathing machinery power scales between linear and square while rocket mass cubically, so a useful air breathing on say a Starship is hard to imagine.