General model of economics, economics as mathematical structure
You may be interested in reading "Economic Models as Analogies", a 2014 article by Itzhak Gilboa, Andrew Postlewaite, Larry Samuelson and David Schmeidler, four well regarded economic theorists. They argue, somewhat contrary to your view of economic theorizing, that economic models are better viewed as "theoretical cases" rather than general rules akin to the laws of physics. Predictions are made by drawing analogies between the world in which the models live and reality. In Section 4 of the paper, they do propose a "model of economic models" that formalizes their argument. Although this model is probably not the one you were looking for, it may help clarify your (mis)perception of the methodology in theoretical economics. 

The paper's abstract is as follows: 


  People often wonder why economists analyse models whose assumptions are known to be false,
  while economists feel that they learn a lot from such exercises. We suggest that part of the
  knowledge generated by academic economists is case-based rather than rule-based. That is, instead
  of offering general rules or theories that should be contrasted with data, economists often analyse
  models that are ‘theoretical cases’, which help understand economic problems by drawing
  analogies between the model and the problem. Thus, economic models, empirical data,
  experimental results and other sources of knowledge are all on equal footing, that is, they all
  provide cases to which a given problem can be compared. We offer complexity arguments that
  explain why case-based reasoning may sometimes be the method of choice and why economists
  prefer simple cases.