Yes, the techniques employed in this paper could potentially be extended to study the complexity of approximately counting other types of graph structures, such as maximal cliques or minimal vertex covers. The foundational approach of using Approximation-Preserving reductions (AP-reductions) can be adapted to analyze the relationships between these different counting problems.
For instance, maximal cliques, like maximal independent sets, are fundamental structures in graph theory, and their counting problem is also known to be #P-complete. By constructing appropriate gadgets and transformations similar to those used in the reduction from #IS to #MIS, researchers could explore the complexity of approximately counting maximal cliques. Similarly, the minimal vertex cover problem, which is closely related to independent sets, could be analyzed using analogous techniques.
The key would be to establish a clear mapping between the structures of these problems and to demonstrate that the complexity of approximating one can be translated into the complexity of approximating another. This could lead to a deeper understanding of the landscape of counting problems in graph theory and their interrelations.