Tensegrity rovers incorporate design principles that give rise to many desirable properties, such as adaptability and robustness, while also creating challenges in terms of locomotion control. A recent milestone in this area combined reinforcement learning and optimal control to effect fixed-axis rolling of NASA’s 6-bar spherical tensegrity rover prototype, SUPERball, with use of 12 actuators. The new 24-actuator version of SUPERball presents the potential for greatly increased locomotive abilities, but at a drastic nominal increase in the size of the data-driven control problem. This paper is focused upon unlocking those abilities while crucially moderating data requirements by incorporating symmetry reduction into the controller design pipeline, along with other new considerations. Experiments in simulation and on the hardware prototype demonstrate the resulting capability for any-axis rolling on the 24-actuator version of SUPERball, such that it may utilize diverse ground-contact patterns to smoothly locomote in arbitrary directions.