Two-step and multistep spin transitions are frequently observed in switchable cooperative molecular solids. They present the advantage to open the way for three- or several-bit electronics. Despite extensive experimental studies, their theoretical description was to date only phenomenological, based on Ising models including competing ferro- and antiferro-magnetic interactions, even though it is recognized that the elastic interactions are at the heart of the spin transition phenomenon, due to the volume change between the low-and high-temperature phases. To remedy this shortcoming, we designed the first consistent elastic model,taking into account both volume change upon spin transition and elastic frustration. This ingredient was revealed to be powerful, since it was able to obtain all observed experimental configurations in a consistent way. Thus, according to the strength of the elastic frustration, the system may undergo first-order transition with hysteresis, gradual, hysteretic two-step or multistep transitions, and incomplete transitions. Furthermore, the analysis of the spatial organization of the HS and LS species in the plateau regions revealed the emergence of complex antiferro-elastic patterns going from simple antiferro-magnetic-like order to long-range spatial modulations of the high-spin fraction. These results enabled us to identify the elastic frustration as the fundamental mechanism at the origin of the very recent experimental observations showing the existence of organized spatial modulations of the high-spin fraction inside the plateau of two-step spin transitions.