This is easily analyzed by asking CBC to include interaction effects in the utility estimation. If using Lighthouse Studio, when you run an aggregate logit, latent class MNL, or HB model, you can click the "gear icon" (the settings icon) within the Analysis Manager, and then click the Attribute Coding link. At the bottom of the Attribute Coding dialog you can see a green "plus" icon for adding interaction effects between 2 attributes at a time.
Remember, to interpret the total effect of two attributes involved in an interaction, you take the main effects and add them to the interaction effects. In other words, interaction effects are the adjustment to main effects to account for interactions between attributes taken 2 at a time.