Self-assembled monolayers of microparticles encoding Archimedean and non-regular tessellations promise unprecedented structure-property relationships for a wide spectrum of applications in fields ranging from optoelectronics to surface technology. Yet, despite numerous computational studies predicting the emergence of exotic structures from simple interparticle interactions, the experimental realization of non-hexagonal patterns remains challenging. Not only kinetic limitations often hinder structural relaxation, but also programming the inteparticle interactions during assembly, and hence the target structure, remains an elusive task. Here, we demonstrate how a single type of soft polymeric microparticle (microgels) can be assembled into a wide array of complex structures as a result of simple pairwise interactions. We first let microgels self-assemble at a water-oil interface into a hexagonally packed monolayer, which we then compress to varying degrees and deposit onto a solid substrate. By repeating this process twice, we find that the resultant structure is not the mere stacking of two hexagonal patterns. The first monolayer retains its hexagonal structure and acts as a template into which the particles of the second monolayer rearrange to occupy interstitial positions. The frustration between the two lattices generates new symmetries. By simply varying the packing fraction of the two monolayers, we obtain not only low-coordination structures such as rectangular and honeycomb lattices, but also rhomboidal, hexagonal, and herringbone superlattices which display non-regular tessellations. Molecular dynamics simulations show that these structures are thermodynamically stable and develop from short-ranged repulsive interactions, making them easy to predict, and thus opening new avenues to the rational design of complex patterns.