Also, if I do run multiple 2- or 3-way ANOVAs, then would I have to correct for multiple comparisons as a result? Would the Holm method work for this?

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Also, if I do run multiple 2- or 3-way ANOVAs, then would I have to correct for multiple comparisons as a result? Would the Holm method work for this?

Run the 4-way ANOVA, and remove non-significant terms from the model. This increases the power for the remaining terms. Most high order interactions are very weak, may be spurious, and are rarely useful unless they occur in a chemical/nuclear environment.

I recommend sticking with the 4-way ANOVA. It is not that difficult to analyze manually by creating the formulas in Excel to create your own ANOVA table. I used to manually calculate them by hand.

I haven't been able to find anything on how to do a 4-way ANOVA.

Here is a more detailed explanation.