Testing for too many interaction effects?
I'm conducting a bayesian Mixed ANOVA and am interested in a two-way interaction effect to test my main hypothesis. However... there are technically four variables I can examine in exploratory analyses (participant gender and gender of person in stimulus videos). I'm aware how computationally intensive testing for a four way interaction effect would be in a bayesian framework, so my question is, is there any consensus on what the maximum number of interaction effects it is reasonable to test for? Are there any disadvantages other than simply the time taken to conduct the analysis?
Many Thanks in advance if anyone knows about this subject.