When Eli Goldratt was working with partners and Certified Associates to develop and document the Theory of Constraints Thinking Processes, he was also working on defining the "Socratic Approach" -- an approach he'd used to great effect in his best seller "The Goal" where readers overwhelmingly felt a kinship with the protagonist Alex Rogo and took ownership in some of the most radical concepts ever presented to manufacturers - the absolute opposite of the resistance that meets most ideas.
As if to validate that there is indeed order in the universe, the TOC Thinking Processes, designed to analyze problems and plan a solution, corresponded (as a solution) to the Layers of Resistance with a degree of precision that was awe-inspiring.
A Good starting point here is to take some time to understand the Theory of Constraints Thinking Processes in their most basic function.
The Current Reality Tree or CRT was originally developed a a Cause-Effect tool that is an order of magnitude more powerful than the Ishikawa diagram or "Ask Why 5 times" technique in its ablity to pin-point a deep rooted core problem responsible for, or contributing substantially to, the existence of a suite of symptom. It's not unusual for a CRT to, in effect, "ask why 20+ times," and fill in the answers in terms of beliefs, policies, procedures, measurements and behaviors.
It can also be used to work the other way ... to take a speculated core problem and validate that the core problem indeed contributes substantially to the target suite of symptoms.
In gaining a buy-in, this becomes a great tool for gaining a buy-in to the real problem - it is a great communication tool, people can see the logic, with every assumption laid out, that absolutely validates that your understanding of the problem is solid; and the logic and the manner of building and presenting the CRT gains a buy-in.
The Evaporating Cloud is a form of conflict diagram that articulates a conflict in the organization and illustrates the shape of the compromises that exist in an effort to mitigate (not eliminate) the effects of the conflict. It shows why the core problem that creates such damaging problems, and probably has done so for years, has gone unresolved. So, it helps cement buy-in to the problem.
However, the Evaporating Cloud also offers managers a methodical way to plan a way out of the conflict - a win/win path that becomes the "direction of the solution," or a good idea. In this, the Cloud is the bridge between dealing with Layers 1 and 2 of Resistance.
The Future Reality Tree or FRT deals directly with two layers of resistance. It provides a step-by-step explanation of everything that will have to be in place, beyond the original "good idea," in order for the target symptoms to be eliminated. In other words, it provides the details and the cause-effect logic to validate that the solution will, in detail, generate the desired outcomes. And, the logic and the manner of building and presenting a FRT gains a buy-in.
It also has a component specially aimed at dealing with potential, negative side-effects that could be the outcome of the solution elements themselves, or the outcome of a successful solution. So in this it deals with the Layer of Resistance addressing the "yes, buts..." of the negative side-effects. So it's the tool to gain a buy-in that the predicted negative side effects will not emerge, which calms a LOT of concerns in people.
The Prerequisite Tree or PRT allows people to articulate every major obstacle they see to every element of the Future Reality Tree that will have to be added, i.e. that doesn't already exist. This by itself is powerful; but it then provides a framework for addressing every one of those obstacles, and if handled correctly it gains a powerful buy-in that the solution is realistic.
How these tools are deployed towards a buy-in depends on some of the nuances of the specific buy-in circumstances.