Conventional RAID solutions with fixed layouts partition large disk enclosures so that each RAID group uses its own disks exclusively. This achieves good performance isolation across underlying disk groups, at the cost of disk under-utilization and slow RAID reconstruction from disk failures. We propose RAID+, a new RAID construction mechanism that spreads both normal I/O and reconstruction workloads to a larger disk pool in a balanced manner. Unlike systems conducting randomized placement, RAID+ employs deterministic addressing enabled by the mathematical properties of mutually orthogonal Latin squares, based on which it constructs 3-D data templates mapping a logical data volume to uniformly distributed disk blocks across all disks. While the total read/write volume remains unchanged, with or without disk failures, many more disk drives participate in data service and disk reconstruction. Our evaluation with a 60-drive disk enclosure using both synthetic and real-world workloads shows that RAID+ significantly speeds up data recovery while delivering better normal I/O performance and higher multi-tenant system throughput.