You can take those interactions that are theoretically meaningful and/or statistically significant.

Dear Joost,

I am not sure exactly what type of analysis you are referring to. If it is multiple linear regression with binary and scale variables you can start by including all the interaction terms using an automated method, such as Backwards elimination. Once this have given you a converged model you should verify it by looking at the residuals and maybe building it from 80% of your data and applying it to the other 20%. Non-normal residuals indicate that your confidence intervals may not be reliable.

However, I agree with Mehmet that your initial model should be guided qualitatively by the meaningfulness of your selected interactions. You should also consider the principle of parsimony (i.e. the simplest model explaining the maximum amount of content).

We have developed a deliberately exploratory  random coefficient (mixed)  approach to counts of complex tables that we argue automatically takes into account multiplicity of testing by shrinking  the Observed/Expected ratios when they are based on small counts ( coming with interactions between predictors)  and are hence unreliable. The result is  precision-weighted estimates that aim to reduce the overall Mean Square Error of the estimates.  

https://www.researchgate.net/publication/266383638_A_model-_based_approach_to_the_analysis_of_a_large_table_of_counts_occupational_class_patterns_in_among_Australians_by_ancestry_generation_and_age_group

https://www.researchgate.net/publication/290434078_Uncovering_interactions_in_multivariate_contingency_tables_a_multi-level_modelling_exploratory_approach

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