The aim of this Letter is to introduce a new optical tweezers approach, called scanning holographic optical tweezers (SHOT), which drastically increases the working area (WA) of the holographic-optical tweezers (HOT) approach, while maintaining tightly focused laser traps. A 12-fold increase in the WA is demonstrated. The SHOT approach achieves its utility by combining the large WA of the scanning optical tweezers (SOT) approach with the flexibility of the HOT approach for simultaneously moving differently structured optical traps in and out of the focal plane. This Letter also demonstrates a new heuristic control algorithm for combining the functionality of the SOT and HOT approaches to efficiently allocate the available laser power among a large number of traps. The proposed approach shows promise for substantially increasing the number of particles that can be handled simultaneously, which would enable optical tweezers additive fabrication technologies to rapidly assemble microgranular materials and structures in reasonable build times.