<p>Solution spaces are sets of designs which meet all design goals. These sets can be structured such that the value of each design variable, or each group of design variables (which are associated with a component), can have its value(s) chosen from this set independently of the others. However, previous works have always been limited, either by restricting the number of design variables per component or by only being applicable to specific system types, such as linearly decomposable systems. Typically, box-shaped solution spaces do not include most the complete solution space, even for 2 dimensions per component. In this work, we present a novel method and algorithm which generates so-called component solution spaces for arbitrary systems and which can contain an arbitrary number of design variables in each component. This is done with a novel strategy called <i>planar trimming</i>, where solution spaces are computed as convex sets for each component in a stochastic manner. To illustrate the applicability of this method, we show examples of 2D and 3D truss structures with requirements on tip deflection and total mass. For these examples, we create admissible regions for the positions of the nodes of said trusses to allow for maximum design freedom in their locations, while ensuring the independence of each node’s position with respect to meeting the requirements. Additionally, we show that the total area/volume of admissible space for each node’s position is significantly larger than box-shaped solution spaces generated with classical methods, and for higher dimensional problems, said improvements are further increased.</p>