As described in the documentation, you can indeed predict combinatorial outcomes using the market simulator within MBC (as long as you have used HB estimation). You need to request combinatorial predictions within the simulator interface (click "Simulate Choice Combinations" then also click the checkbox to "Display Individual Results When Available".
One of the output tabs will show the combinatorial predictions by respondent. Then, analyze the output representing the individual-level combinatorial predictions using a tabulation software (or you could even construct this counting analysis within Excel) so that you can tabulate 2-way frequencies between the target dependent variables of interest.
As a side note: combinatorial prediction accuracy will be better if you initially formulate the dependent variables as combinatorial combinations (combinatorial dependent variables), where you collapse certain groupings of binary variables that seem to make sense to combine. Those collapsed combinatorial coded dependent variables shouldn't exceed a few dozen potential outcomes, however. For example, you might code up 4 dependent binaries as a single 16-level dependent variable.