This page contains a number of designs from the LRA's past.
The Cluster rocket was a design which simultaneously used different sizes of solid-fuel motors for propulsion
The Vertigo rocket skipped the parachute, opting instead for five carbon-fiber blades which swung out at apogee and allowed the rocket to autogyro safely to the ground.
A "drag-race" rocket, this design was proportionately much wider than standard.
A "parasitic" design, this interesting take on staged rockets is actually two rockets in one; after the lower engine burns out, a smaller rocket buried in the upper section of the first stage rocket launches from a slotted nosecone.
Being one of our oldest designs and no longer in the LRA's possession, documentation on this design is...poor. Presumably, the booster rockets fired a set delay after the main burned out.