Limitation: Cannot search for (anthro OR taur) AND (female OR intersex) i.e. (anthro ~female ~intersex) and (taur ~female ~intersex) in a single result.
This search should show posts tagged with BOTH either anthro or taur, AND female or intersex.
If I search ~anthro ~taur ~female ~intersex, the search shows results of posts tagged with female, or taur, or intersex, or anthro individually.
Lack of tag pairing is a tremendous loss to the functionality and power of the search function.

I understand such a function exists in blacklists, where it will only exclude posts containing BOTH of your criteria, but not individually, as long as they are entered on the same line.
e.g. I can use -anthro -fox to exclude posts tagged EITHER anthro or fox. In blacklists, it only excludes posts that contain BOTH, so you can still see posts tagged with either one individually. i.e. -(anthro fox)

There is also the issue of incorrectly tagged posts. Let's say I want to find posts containing a feral domestic_cat, but the post is not tagged feral.
If I search domestic_cat, I will receive results containing a domestic_cat in all forms. If I try and subtract forms, I will lose posts that may contain a feral domestic_cat if they also include that other form. With a compound search, I could at least remove posts of a (solo anthro domestic_cat) without removing solo domestic_cat posts, or domestic_cat posts containing other characters that are anthro.

Additionally, we lack precision tags to bulk exclude other tags.
e.g. Only_Feral would show results containing ferals, and no other forms. As it stands, you need to subtract all other forms to get such a result.

This should be a logical argument, not something that would require re-tagging all posts. The Only_* search argument should simply imply the exclusion of the alternative tags of the same type. You might not implement this for every tag, but it would certainly simplify things for gender, form and other short lists of large encompassing tag types.

Bonus unsolvable problem?
Consider this use-case, where you are searching for posts containing a feral domestic_cat. Due to re-tagging issues, we won't introduce the new tag feral_domestic_cat.
However, if you search for domestic_cat feral, any post containing 2 characters could feature a non-feral domestic_cat. Similarly, if you -anthro -human - humanoid, you are now removing ALL posts containing those tags, even if they include a feral domestic cat.