Aaron Benanav and Ryan Lee of Cornell University have published a working paper on a microeconomic theory that could serve as the foundation for a new, multidimensional economics.
More specifically, Benanav conceives of a new, multidimensional economics as being the theoretical foundation for his proposal for a multi-criterial socialism, which you can read about here, here and here.
A summary of the working paper can be found below:
Classical rational choice theory assumes preferences are complete, presupposing that an agent’s evaluative considerations have a common scale. We drop completeness and develop a normative theory of rational choice for agents whose values are plural and incommensurable. The resulting individual choice problem is characterized as the formal dual of Arrovian social choice. The agent’s value structure determines a majority tournament whose cycle topology partitions choice behavior into three classes: classical optimization, recovered when values converge; the hard choice, in which value conflicts are structurally isolated; and the tragic choice, in which conflicts are entangled and all classical consistency properties fail. Violations of classical consistency conditions are rational responses to value conflict rather than departures from rationality.
You can read the working paper here.