One advantage that solid rockets have over liquid fuel rockets is that the solid propellant is typically very dense compared to liquid propellant. This means that even though solid rockets tend to have notably lower specific impulse than liquid rockets, the same level of total performance can be packed into a smaller volume. This is one important reason why space launch rockets are typically liquid propellant while ICBMs and especially SLBMs are solid propellant… the doesn’t matter much for space launchers, but space in a submarine is at a premium.
Even so, it’s always good to fine a way to reduce the volume consumed by a solid rocket even further. A proposal from JPL in 1972 produced concepts for staged solid rockets that would have made substantial reductions in vehicle size by effectively packing solid rockets into each other. The nozzle of Stage II would serve as part of the forward bulkhead for the motor of Stage I; the forward bulkhead of Stage II would serve as the nozzle of Stage III, and so on. Really quite clever. A downside is that the nozzles would be pretty heavy, but I suspect that with proper mechanical and propellant design, this could have produced substantial gains in terms of size and overall mass.
Evolution of the concept from a set of conventional s tages.
Detailed view of the concept. Note that the stages would be separated by the detonation of a ring of linear shaped charge. This is pretty standard in large-scale rocketry.