Multiple-beam laser processing may be performed on a workpiece using at least first and second laser beams with different characteristics (e.g., wavelengths and/or pulse durations). In some applications, an assist laser beam is directed at a target location on or within the workpiece to modify a property of the non-absorptive material. A process laser beam is directed at the target location and is coupled into absorption centers formed in the non-absorptive material to complete processing of the non-absorptive material. Multiple-beam laser processing may be used, for example, to drill holes in a substrate made of alumina or other transparent ceramics. In other applications, multiple-beam laser processing may be used in melting applications such as micro-welding, soldering, and forming laser fired contacts. In these applications, the assist laser beam may be used to modify a property of the material or to change the geometry of the parts.