Based on decades of single-spacecraft measurements near 1 au as well as data from heliospheric and planetary missions, multi-spacecraft simultaneous measurements in the inner heliosphere on separations of 0.05-0.2 au are required to close existing gaps in our knowledge of solar wind structures, transients, and energetic particles, especially coronal mass ejections (CMEs), stream interaction regions (SIRs), high speed solar wind streams (HSS), and energetic storm particle (ESP) events. The Mission to Investigate Interplanetary Structures and Transients (MIIST) is a concept for a small multi-spacecraft mission to explore the near-Earth heliosphere on these critical scales. It is designed to advance two goals: (a) to determine the spatiotemporal variations and the variability of solar wind structures, transients, and energetic particle fluxes in near-Earth interplanetary (IP) space, and (b) to advance our fundamental knowledge necessary to improve space weather forecasting from in situ data. We present the scientific rationale for this proposed mission, the science requirements, payload, implementation, and concept of mission operation that address a key gap in our knowledge of IP structures and transients within the cost, launch, and schedule limitations of the NASA Heliophysics Small Explorers program.