Yield gap analyses of individual crops have been used to estimate opportunities for increasing crop production at local to global scales, thus providing information crucial to food security. However, increases in crop production can also be achieved by improving cropping system yield through modification of spatial and temporal arrangement of individual crops. In this paper we define the cropping system yield potential as the output from the combination of crops that gives the highest energy yield per unit of land and time, and the cropping system yield gap as the difference between actual energy yield of an existing cropping system and the cropping system yield potential. Then, we provide a framework to identify alternative cropping systems which can be evaluated against the current ones. A proof-of-concept is provided with irrigated rice-maize systems at four locations in Bangladesh that represent a range of climatic conditions in that country. The proposed framework identified (i) realistic alternative cropping systems at each location, and (ii) two locations where expected improvements in crop production from changes in cropping intensity (number of crops per year) were 43% to 64% higher than from improving the management of individual crops within the current cropping systems. The proposed framework provides a tool to help assess food production capacity of new systems (e.g. with increased cropping intensity) arising from climate change, and assess resource requirements (water and N) and associated environmental footprint per unit of land and production of these new systems. By expanding yield gap analysis from individual crops to the cropping system level and applying it to new systems, this framework could also be helpful to bridge the gap between yield gap analysis and cropping/farming system design.