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Image/sketch completion is a core task that addresses the problem of completing the missing regions of an image/sketch with realistic and semantically consistent content. We address one type of completion which is producing a tentative completion of an aerial view of the remnants of a building structure. The inference process may start with as little as 10% of the structure and thus is fundamentally pluralistic (e.g., multiple completions are possible). We present a novel pluralistic building contour completion framework. A feature suggestion component uses an entropy-based model to request information from the user for the next most informative location in the image. Then, an image completion component trained using self-supervision and procedurally-generated content produces a partial or full completion. In our synthetic and real-world experiments for archaeological sites in Turkey, with up to only 4 iterations, we complete building footprints having only 10-15% of the ancient structure initially visible. We also compare to various state-of-the-art methods and show our superior quantitative/qualitative performance. While we show results for archaeology, we anticipate our method can be used for restoring highly incomplete historical sketches and for modern day urban reconstruction despite occlusions.