Knowledge on the interaction between plants and organic amendments is critical for the basic understanding of agroecosystems sustainability. Organic amendments are of great interest in agriculture by virtue of their ability to restore lost soil organic carbon in eroded or conventionally cultivated soils. The major objective of this study was to demonstrate and model the differential response of crop species to organic amendments. Despite the potential of such an interaction to improve crop production, it has never been formally demonstrated in a planned experiment. A two-year greenhouse experiment set as 3×3×5 factorial in a strip-split plot design was conducted. The effects of crop species, type of organic amendment, and application rates on grain yield of soybean, canola, and wheat were evaluated. To account for the asymmetry of the concave responses of soybean, mathematical transcendental models were fitted, for the first time, to yield data. The interaction between crop species and amended soils was highly significant. Soybean displayed concave transcendental yield responses whereas canola and wheat exhibited negative exponential responses, irrespective of the type of amendment. Turkey compost outperformed turkey litter and beef manure by 30% and 52%, respectively, with respect to soybean production; whereas turkey litter outperformed turkey compost and beef manure by 144% and 264%, respectively, with respect to canola and wheat production. It is concluded that in greenhouse settings and perhaps field conditions, growth and development of crop species can be enhanced by matching the specific characteristics of organic amendments to the specific nutrients demand of crop species.