Based on what Scrambler has posited, I don’t think the problem can easily be solved after a manual insertion of Xtreme into the process, given that both the relevant pages and links are from WP Core.
I see two possible solutions, though both are of dubious merit….
When one selects a category or tag from the Xtreme page-with-posts, the link takes one to a WP Page for which there is no doubt a template available somewhere in the WP core.
If you can find and modify that template and add your 5 column there as the format default, then that may work.
However, there’s a good chance that that template is used for other things and the result could break the site.
One other option is to re-write the “Category” or” Tag” link that one clicks, and reroute that link path to a known Page Template which does as needed, and provides 5 columns and displays posts.
Again this requires hacking WP Core links and is really not recommended, even if technically feasible.
If i can think of a more reasonable solution I’ll pass it along, but I don’t think there are many, if any, stock solutions out there that provide second level sortings you desire.
Regards.