Let me first distinguish between two-stage and multi-stage models by emphasizing on two issues, namely the type of uncertainty covered by each model and the sources of stochastic parameters. In two-stage models, you have to assume that stochastic parameters are stationary after being observed. On the other hand, multi-stage models assume a non-stationary behavior. Regarding the sources of stochastic parameters, they usually come from either historical data (usually translated into probability distributions or scenario) or experts’ judgment (directly translated into a small number of scenarios).
Following the case of scenarios created by experts, I believe your only option is two-stage stochastic programming models as it is hard, if not impossible, to create valid scenarios corresponding to a non-stationary behavior. This is usually the case for strategic problems where only a few scenarios are considered in detail. Now if you have enough historical data to fit probability distribution functions or create meaningful scenarios, you have to decide your modeling approach (i.e., choosing between two- stage and multi-stage models).
Now, let’s review the issue of stochastic parameters behavior. A stationary behavior is usually modeled as a two-stage stochastic program. This is in accordance with the way we make a decision. You anticipate some uncertainty and take some precautions. Then you observe a realization of uncertainty and react accordingly and correct your mistakes (i.e., known as the recourse action in SP literature). A non-stationary behavior is better modeled as a multi-stage stochastic program. Here, you’re making some day-to-day decisions, such as financial trading, inventory control, or vehicle routing. Let’s take the example of financial trading. Each day, you invest in some assets, gain/lose some money due to uncertainty realized that day. Then, you keep/change your position in anticipation of what is going to happen tomorrow (which might not be similar to what happened today).
Your location-transportation problem is a good example of two-stage models, where you invest before knowing customers’ demands and then react (i.e., change your transportation plan) in accordance with customers’ actual demands. Here, even if you model the problem as a multi-stage problem, all stages after the first one look the same as they are essentially doing the same thing (i.e., transporting goods from warehouses to customers in the later stages vs. building warehouses in the first stages). The only way you could make this problem a multi-stage one is to assume that you could build new warehouses in every stage.
Based on the above, I don’t think a multi-stage problem could be correctly modeled as a two-stage problem. In addition, I've not seen your described approach formally stated anywhere in the literature before. Although it seems to be a practical heuristic for solving a complex problem. However, following the above discussion, I do not think it is necessarily a very good heuristic for the inherently operational problems.
Finally, I think reading section 1.5 of King and Wallace's "Modeling with Stochastic Programming" could shed more light into your question.
PS. As one might confuse the notion of time periods and stages in stochastic programming, I refer them to the following paragraph from King and Wallace's book on page 16.
“We should not confuse information stages with time periods. Stages
model the flow of information; time periods represent the ticking of
the clock in a model. Stages, on the other hand, are points in time
where we make decisions in the model after having learned something
new.”
