I learned a lot from reading the 1951 Soviet study on rocket staging, done at the Steklov Mathematical Institute. It was the basis for the design of the R-7, but it thuroughly considered the general problem of extending rocket range by discarding pieces of its structure during flight:
If you launch three identical rockets on the same trajectory, they should go the same distance in the same time. If you bolt them together and launch them, you get the same result, no increase in range. So how can you gain anything from putting rocket stages in paralle?

The simplest case is what the R-7 did, and what the Delta IV heavy does. Make the boosters lighter, but give them the same engine thrust. This means they contribute more to the acceleration, because they have a higher a = F/m thrust to mass ratio. The Russians called this design the "carrying packet".
But Tikhonravov had an even better idea in the 1940s. Imagine that when the Delta IV takes off, all three engines are fed from just the tanks in the two outer boosters. When they run out of fuel, they are ejectged, and the central stage continues, using its own completey full fuel tank. They called this design the "feeding packet", but to the best of my knowledge, nobody has ever implemented it.
YOu can argue that a feeding packet design is more efficient than sequential stages, because the second stage engine is working all the time, instead of being dead weight during the first-stage burn.
To optimize these concepts, the ratio of masses of the stages can be optimized, using three identical stages is not the best, it is better if the central "second stage" is smaller.