Hi @chacha,
The definition of a 'core microbiome' is not well defined (if at all) and may vary greatly across disciplines. In addition, it is very dependent on the questions being asked from the experiment/data, so I imagine its hard to justify creating pre-made plugins for downstream analysis of it without some evidence-based justification. With that disclaimer out of the way...
Which analysis/test do you have in mind exactly?
If you are looking to obtain a feature table with just the core features, you can perform the feature-table core-features on your feature table, download the feature list (the TSV file produced by the resulting .qzv output) and use the identified Feature IDs in there through the identifier-based filtering step (tutorial for that here). This will give you a table with only the core features which you can use for downstream analysis as usual.
That's one method using the core-features approach. I think if all you want is a feature table with features that are present in some fraction of all your samples and not the other details and calculations provided by the core-features function, you might be be able to do this faster using the feature-table filter-features directly (ex here).
Hope this gets you started!