Due to their outstanding characteristics, additive manufacturing processes are attracting increasing industrial interest. Among these processes, laser metal deposition (LMD) is an innovative technology for the production of metal components. In order to create three-dimensional parts, wire or powder is deposited layer-wise onto a substrate. When wire is used as feedstock, major drawbacks of the powder-based process, such as the low material usage, contamination of the process cell with metal powder, and health or safety issues, can be overcome or even avoided. In addition, recent developments in laser optics allow for a coaxial wire feeding in the center of an annular laser beam. This eliminates the strong directional dependence of the process when feeding the wire laterally. However, wire-based LMD is highly sensitive to process disturbances, which impedes its broader industrial application. Since it is necessary to completely melt the fed wire to achieve a stable process, self-regulating effects such as overspray in powder-based LMD are not present. In contrast to the widely investigated thin walls, the build-up of multi-track solid structures poses a particular challenge. Therefore, process strategies for producing such solid structures are presented in this paper. The experiments were carried out using a laser processing head that enables coaxial wire feeding (CoaxPrinter, Precitec). By systematically varying the lateral overlap between adjacent weld beads, it was shown that an optimum exists at which minimum surface waviness is achieved. Based on this, defect-free multi-layer solid components could be generated in a reproducible manner. During the process, the melt pool temperature was evaluated using a pyrometer. Furthermore, a microscopic examination of the resulting parts was conducted. The results obtained show the need for process monitoring and control, for which a novel and holistic approach has been developed.