It will be hard to improve on what Frank wrote above. I’ll just post a link to the short thread that occurred here a few months ago were I posted some references to this issue:
If neither 1. ordering the research questions or 2. doing an alpha spending adjustment are acceptable, it might be worth considering the FDR procedure. The following is open access:
Watson, J.; Robertson, D. (2020) Controlling type I error rates in multi‐arm clinical trials: A case for the false discovery rate. Pharmaceutical Statistics (link)
Bradley Efron has done much work in giving the FDR an Empirical Bayes interpretation.