Additive manufacturing is moving towards the use of machines with five or more axes but is limited by the inability to easily generate print paths. This usually requires the creation of custom G-code in order to utilize five-axis printing. However, as additive manufacturing begins to utilize five-axis printing for scenarios such as repair, modification, or composite printing, the existing print surfaces become potential obstacles that need to be accounted for in path planning. This paper shows a novel way of expanding the capabilities for printing on complex, concave parts, in order to prevent collisions between the printer and the part. This is achieved through two main steps: Area Refinement, and Angle Determination. During Area refinement, the proposed print area is altered based on the geometry of the print surface, along with printer parameters. This results in a print region that is feasible with the given machine configuration and geometry, that will not attempt to print too close to any existing surface in the presence of concavities. During Angle Determination, the finalized print paths are adjusted to set a nozzle orientation that prevents the machine from colliding with the part. In this paper, we present the algorithmic details behind these approaches and show computational results for two complex concave geometries.