The Einstein-Hilbert action of general relativity is uniquely determined by general covariance and the requirement that only second derivatives in the metric appear. Yang-Mills theory can be motivated in a similar way. In the original paper of Scherk, Julia, Cremer there are some arguments given from which they deduced the form of the action. They are only sketched however. Is there a more complete exposition of the derivation in the literature, or possibly even a uniqueness result as in the case of general relativity or Yang-Mills theory?
A beautifully conceptual derivation of 11d SuGra was given in
- Riccardo D'Auria, Pietro Fré, Geometric Supergravity in D=11 and its hidden supergroup, Nuclear Physics B201 (1982) 101-140 (nLab)
using the excellent supergeometric methods later laid out in their textbook
- Leonardo Castellani, Riccardo D'Auria, Pietro Fré, Supergravity and Superstrings - A Geometric Perspective World Scientific, 1991 (nLab)