Concentrated ionic solutions present a potential improvement for liquid electrolytes. However, their conductivity is limited by high viscosities, which can be attenuated via cosolvation. This study employs a series of experiments and molecular dynamics simulations to investigate how different cosolvents influence the local structure and charge transport in concentrated lithium bis(trifluoromethane-sulfonyl)imide (LiTFSI)/acetonitrile solutions. Regardless of whether the cosolvent's dielectric constant is low (for toluene and dichloromethane), moderate (acetone), or high (methanol and water), they preserve the structural and dynamical features of the cosolvent-free precursor. However, the dissimilar effects of each case must be individually interpreted. Toluene and dichloromethane reduce the conductivity by narrowing the distribution of Li+-TFSI- interactions and increasing the activation energies for ionic motions. Methanol and water broaden the distributions of Li+-TFSI- interactions, replace acetonitrile in the Li+ solvation, and favor short-range Li+-Li+ interactions. Still, these cosolvents strongly interact with TFSI-, leading to conductivities lower than that predicted by the Nernst-Einstein relation. Finally, acetone preserves the ion-ion interactions from the cosolvent-free solution but forms large solvation complexes by joining acetonitrile in the Li+ solvation. We demonstrate that cosolvation affects conductivity beyond simply changing viscosity and provide fairly unexplored molecular-scale perspectives regarding structure/transport phenomena relation in concentrated ionic solutions.