We present resolved H I synthesis maps from the Very Large Array of three interacting dwarf systems: the NGC 3664 dwarf pair, the NGC 3264 dwarf pair, and the UGC 4638 dwarf triplet. All three dwarf systems are captured at various stages of interaction and span a range of environments. We detect clear hallmarks of tidal interactions through the presence of H I bridges and diffuse H I extensions that surround the dwarfs. We overlay the H I data on Pan-STARRS r-band images and find further evidence of tidal interactions through coincident distorted H I and tidal stellar features in NGC 3264 and UGC 4638, and an unwound spiral arm pointing toward its smaller companion in NGC 3264. In UGC 4638, both the gas and diffuse stars are extended to similar radii east of the primary, which could indicate that the smaller dwarf in the system has already completed one pass through the primary. We additionally find that our three systems, and those from the Local Volume TiNy Titans survey, are not H I deficient and thus the interaction has not resulted in a loss of gas from the systems. A comparison with noninteracting dwarf galaxies shows that the interactions have a significant impact on the kinematics of the systems. Our new resolved H I kinematics, combined with detailed stellar and H I morphologies, provide crucial constraints for future dynamical modeling of hierarchical mergers and the baryon cycle at the low-mass scale.