I assume he might have been talking about things like graph/systems/game theory or more mathematically oriented discourse analysis. Has anyone actually found such an approach useful?
I'm gonna go into "danger, Will Robinson" territory and do something I'm usually reluctant to do. I was a part of a working group thinking about emergence, complex adaptive systems, networks and information theory for a few years here in a local consortium. I ended up being asked to think about the implications of complexity theory for history, and I chose to address that primarily in terms of how it affects our views of causation. https://works.swarthmore.edu/cgi/viewcontent.cgi?article=1001&context=fac-history
But if I can extend that a bit into some work I'm trying to finish now, I would argue that there is a "rigorous" conception of microhistory that relates to complexity theory and emergence.
Emergence as an idea relies on the proposition that many simultaneous small actions by agents may produce complex structures that the agents did not intend to create and had no 'blueprint' for creating. These structures may persist and constrain the future action of future agents even if no one had any awareness that they were contributing through microhistorical action to the end result.
That seems to me to be what Levi may have had in mind. Taking this perspective is actually setting yourself against the kind of work that quantitative social sciences do when they seek to precisely identify the specific causal weight of specific variables in creating outcomes. If you commit to this perspective, you are accepting that you cannot and should not try to isolate variables and assign them greater or less weights. That seems to me a good precursor for a rigorous interest in microhistory--in the acceptance of the idea that the actions of individual agents may be momentously important (or interestingly trivial) while shucking off the obligation to use quantitative methods to rank them as one or the other.