Matlab: How to create one figure from multiple saved boxplot figures

I have seen a number of similar questions, but none of the solutions have been able to do quite what I need. I have a process that loops through a variable number of data sets. In each pass through the loop, a data set is loaded, a box plot is created (using the `boxplot` command), the figure is saved, and the data is cleared.

Because the data sets are so large, and because the number of plots is variable, loading all the data at once is an issue in terms of memory and time.

For the sake of simplicity, let's say I have two saved figures, both of a box plot. Each plot is at the default location on the x-axis because, in reality, the process creates a variable number of plots and the comparison could be between any number of plots from any number of code executions. If I can merge the .fig files, I should end up with one box plot on top of the other. I had partial success with the following question/answer. The plots were in the same location, but one had the xtick label ('1') directly below the box plot, while the other had the xtick label ('1') offset to the left.

How to merge two figure files into a single file

If I can get that merge worked out, I then have to be able to shift the second box plot to the right so they do not overlap. Translating that to my actual problem should be fairly straightforward, as I will just have to use a loop to move subsequent plots to the right one x-value.

The final issue will be adding xtick labels for each box plot at the end. I am not sure how I would do this with multiple overlapping figures now in one figure.

Thank you for the help and suggestions.

Matt