Laser drilling and cutting of materials is well established commercially, although its throughput and efficiency limit applications. This work describes a novel approach to improve laser drilling rates and reduce laser system energy demands by using a gated continuous wave (CW) laser to create a shallow melt pool and a UV ps-pulsed laser to impulsively expel the melt efficiency and effectively. Here, we provide a broad parametric study of this approach applied to common metals, describing the role of fluence, power, spot size, pulse-length, sample thickness, and material properties. One to two order-of-magnitude increases in the average removal rate and efficiency over the CW laser or pulsed-laser alone are demonstrated for samples of Al and stainless steel for samples as thick as 3 mm and for holes with aspect ratios greater than 10:1. Similar enhancements were also seen with carbon fiber composites. The efficiency of this approach exceeds published values for the drilling of these materials in terms of energy to remove a given volume of material. Multi-laser material removal rates, high-speed imaging of ejecta, and multi-physics hydrodynamic simulations of the melt ejection process are used to help clarify the physics of melt ejection leading to these enhancements. Our study suggests that these high-impulse multi-laser enhancements are due to both laser-induced surface wave instabilities and cavitation of the melt for shallow holes and melt cavitation and ejection for deeper channels.