Generating game levels via constraint satisfaction can become slow as levels grow large. In this work, we explore constraint-based generation of large levels by iteratively extending smaller intermediate levels. In each iteration, a new segment is created by generating a new, larger, intermediate level. The tiles and solution path at the beginning of the new intermediate level are constrained to match the previous intermediate level. We evaluated our approach using three games and two low-level solvers. We found that generating a level using more segments improves performance up to a point, and then decreases performance. We also saw a slight but noticeable decrease in the tile-based differences between levels generated as the number of segments increases, and saw that later segments usually took more time to generate than earlier segments.