Experimental designs typically rely on simplified independence assumptions about interference between study subjects. However, when non-trivial interference exists, relying on such assumptions can lead to increased bias and error in estimates. This realization has led to the study of networked experiments, which allow researchers to explicitly model the exposure between study subjects. Motivated by a real-world application, we propose a novel multilevel methodology for modeling and minimizing interference in the design phase of networked experiments. By constructing a network based on the historical communication and affiliation patterns, we model the exposure pathways between subjects using network communicability approach and derive corresponding pairwise interference weights. Using this model we derive a principled experimental design methodology for selecting arbitrary number of treatment groups with minimal intergroup interference. We demonstrate how this problem can be solved via efficient transformation into heaviest k-subgraph problem (HkSP). Further, we formalize two extensions of the problem and propose a modified HkSP heuristic for solving the optimization problem. The resulting design approach accommodates for both individual-level analysis via existing inference under interference frameworks, as well as makes possible studying diffusion dynamics as heterogeneous treatment effects at the neighborhood level. Our results from benchmarks in synthetic networks show that both the interference minimization framework as well as the modified heuristic work as expected and achieve high performance in majority of benchmarks. Additionally, we apply the method in two real life networks of different scale, and particularly in a case study we demonstrate how the method can be applied in realistic experimental context in a communication experiment in Twitter. While the benchmarks indicate good performance, we do also identify fundamental limitations to the approach most of which relate to the combinatorial complexity of the underlying optimization problem and become restrictive with increase in system size. We discuss and propose a set of different optimization strategies and show that with careful contextual consideration these limitations can be overcome even in moderately large networks.