I'm trying to fit a model with one response variable and 11 predictors. Of these 11 predictors: 5 are continuous, 4 are dichotomous and 3 are categorical (containing between 3-7 different categories, which I've coded with dummy variables). I'm having a difficult time trying to figure out which interaction terms to include in the maximum model. Any hints would be greatly appreciated!
Actually, there is not a statistical procedure to indicate what interactions you should consider to your model. Instead, it is the underlying theory that should indicate the phenomena that deserves to be studied.
You should keep in mind that any additional interaction term in the model decrease the significance of the remaining terms. Further, in case that an interaction between two factors will proved to be statistically significant then the main effects of the involved factors (if also statistically significant) should be interpreted with caution since they represent the difference in the dependent variable only for the level of the other factor that correspond to the zero value.
Thus, it also make sense to test a model containing only interaction terms if this is consistent with your research goals.
Finally, keep in mind that order to check the significance of a model with too many terms you should also have an adequate large sample.
In your setting, if your study is of exploratory nature and if your sample is big enough I would consider a model with all 11 predictors as main effects and all 2 way interactions between dichotomous variables (easily interpreted if significant) while I would also considered additional interactions among dichotomous and categorical variables only if they represent interesting research questions in the context of the underlying theory.
Considering the question posed in the comment, it is not suggested to repeat the procedure excluding the part of the model that happened to be not significant, either if this part are some values of a categorical variable or some unrelated independent variables that happened to have significance over 0,05. Doing so, you admit that not statistical significance mean not causation (not correct) while this will definitely increase the significance of the remaining terms, and you may finally find a model where all coefficients are statistically significant but without a theoretical explanation since the criterion that you applied to formulate this model was purely statistical, thus based on the sampling error!
To summarize, use the theory of your field and formulate a model trying to test the hypotheses that emerges from your theoretical study and just report what you find.
Finally, please have a look at the answer of a similar question that I posted in the past!
I hope that the above helps.