One possibility would be to have 2 lists - one lists all possible entries the other modifies the first list based on selections made thus far
To outline above by means of very simple example (which hopefully mirrors your set up in simplistic form):
the above represents all possible items.
In Sheet2!D1:D2, Sheet2!F1:F2 & Sheet2!H1:H2 we will have Data Validation with each cell sharing the same Source list.
The Source List will of course be Sheet1!B1:B6 rather than Sheet1!A1:A6.
To generate the second list:
Next we create a Dynamic Named Range such that the final list includes only valid entries
Finally we go to Sheet2 and create our DV cells - we select D1:D2, F1:F2 & H1:H2 and apply the following Validation rule:
You will find that as you make selections in these cells the options available in the remaining cells become more and more restricted.
I have attached a working example of the above.
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