A material (e.g., proppant) handling system includes a storage container, a mechanical conveyor system, and a pneumatic conveyor system. The mechanical conveyor system is configured to convey material from an unloading station to a conveyor system discharge and into an inlet of the storage container (e.g., at an elevation that is higher than the unloading station). The pneumatic delivery system is configured to deliver material from the storage container to an off-system destination (e.g., a silo or the like), pneumatically. In a typical implementation, the storage container, the mechanical conveyor system, and the pneumatic conveyor system are all on, or connected to, or supported by one common chassis.