The firm in classical economics

On twitter Per Bylund wrote:

I'm increasingly convinced that the social sciences need to be reintegrated. Its universal framework should be based on classical economics.
— Per Bylund (@PerBylund) March 7, 2014

This is an interesting idea but I would ask Per, as theory of the firm man, what the theory of the firm would look like if it is to be based on classical economics. Mark Blaug when so far as to write that the classical economists "had no theory of the firm". Micheal H. Best writes, "Adam Smith did not elaborate a theory of the firm." Smith famously opens The Wealth of Nations with a discussion of the division of labour at the microeconomic (pin factory) level but quickly moves the analysis to the market level. When discussing Smith's approach to the division of labour McNulty comments,

“[h]aving conceptualized division of labor in terms of the organization of work within the enterprise, however, Smith subsequently failed to develop or even to pursue systematically that line of analysis. His ideas on the division of labor could, for example, have led him toward an analysis of task assignment, management, or organization. Such an intra-firm approach would have foreshadowed the much later−indeed, quite recent−efforts in this direction by Herbert Simon, Oliver Williamson, Harvey Leibenstein, and others, a body of work which Leibenstein calls “micro-microeconomics”. [ ...] But, instead, Smith quickly turned his attention away from the internal organization of the enterprise, and outward toward the market and the realm of exchange, perhaps because he found therein both the source of division of labor, in the “propensity in human nature ...to truck, barter and exchange” and its effective limits”

A quick search of the second edition of Edwin Cannan's "History of the Theories of Production and Distribution in English Political Economy from 1776 to 1848" showed that the only time the word firm appears is when Cannan says that an author "would have been on firm ground". The use of the world company or corporation seems to only appear when Cannan is talking about the meaning of the word capital as being the "funds of a trader, company, or corporation".

What this suggests to me is that Blaug is right. As Foss and Klein have noted classical economics was largely carried out at the aggregate level with microeconomic analysis acting as little more than a handmaiden to the macro-level investigation,

“[e]conomics began to a large extent in an aggregative mode, as witness, for example, the “Political Arithmetick” of Sir William Petty, and the dominant interest of most of the classical economists in distribution issues. Analysis of pricing, that is to say, analysis of a phenomenon on a lower level of analysis than distributional analysis, was to a large extent only a means to an end, namely to analyze the functional income distribution”.

With no real emphasis on microeconomics how can a theory of the firm develop? Thus it is not clear what a theory of the firm would look like if based on classical economics.