We present a follow-up study on our unified visuomotor neural model for the robotic tasks of identifying, localizing, and grasping a target object in a scene with multiple objects. Our Retinanet-based model enables end-to-end training of visuomotor abilities in a biologically inspired developmental approach. In our initial implementation, a neural model was able to grasp selected objects from a planar surface. We embodied the model on the NICO humanoid robot. In this follow-up study, we expand the task and the model to reaching for objects in a three-dimensional space with a novel dataset based on augmented reality and a simulation environment. We evaluate the influence of training with auxiliary tasks, i.e., if learning of the primary visuomotor task is supported by learning to classify and locate different objects. We show that the proposed visuomotor model can learn to reach for objects in a three-dimensional space. We analyze the results for biologically-plausible biases based on object locations or properties. We show that the primary visuomotor task can be successfully trained simultaneously with one of the two auxiliary tasks. This is enabled by a complex neurocognitive model with shared and task-specific components, similar to models found in biological systems.