Sounds interesting!
But I don't know of anything immediately that would help you. Maybe we can discuss it some and think about different ideas for you to search for.
To start, can you explain a bit more?
Borrowing usually is boring (structurally)-- words are borrowed with some small phonetic adjustments to nativize them, and then they're used as wholes.
But sometimes borrowing results in reanalysis and integration of other parts. For example:
1. Sometimes phonemes can be borrowed-- eventually nativization is weakened (via strong bilingualism?) and sounds are borrowed with the words. (Think about English ʒ from French loanwords.)
2. Sometimes morphology is borrowed-- octopi is not the original Greek plural, but it's modeled by analogy on some Latin plurals-- we've borrowed the Latin plural formation rule -us > -i.
On the other hand, sometimes borrowed words are reanalyzed (via 'backformation' usually?) as complex words that can be morphologically active. One of the best examples I know of is in Swahili:
The word for 'book' is kitabu, clearly borrowed from Arabic kitaab with some sound adjustments (no closes syllables, no long vowels). What gets really interesting is the plural-- in Arabic it's kutub (via the root and pattern system, somewhat irregular but still following a limited pattern).
In Swahili, the plural is vitabu. Swahili is a prefixing language and plurals are formed based on noun class-- each semantic class has two halves: singular and plural. So the "ki-vi" class is the one where singulars are (usually) marked by ki and the plurals are (usually) marked by vi. So why not-- it starts with "ki", and it roughly matches the semantics of that class (which are vague anyway), and the plural can be vitabu!
Another example, perhaps even more striking is the word "vilabu", which is a cognate (well, via borrowing) of English clubs (as in "go to the club"). "club" was borrowed as "kilabu", then that form was reanalyzed as being a singular ki-vi class noun, so the plural is "vilabu"!
Alternatively, sometimes nothing can happen. An example that comes to mind (I'd have to look up the exact word) is the repluralization 3 or 4 times of an original word in Latin meaning "leaf" (I think). It was usually used in the plural in Latin referring to something like "foliage" on a tree, then borrowed into one of the Romance languages as a singular; the plural form was then used for multiple trees (or forests or something); and then it was borrowed into Tagalog (or something like that) as a singular; and eventually it got a new plural in Tagalog!
All of that is based on a vague memory of an example from a few years ago. So let me know if you want me to try to actually track that one down.
Finally, there's also the interesting case of what appears to be a borrowing grammar-- arbitrary conventions based on perceived relationships between languages. There's no obvious reason why English "-tion" should be borrowed into Spanish as "-ción", but it is. This is due to frequent mappings between the two for historical reasons. That doesn't explain why it's still active in borrowing (it shouldn't be, at just a sound-based level). Also I believe that Russian borrowings of German use h>g sometimes because of analogy to pairs like hospital/gospital that happen to exist. Some languages, such as Japanese, have very well defined borrowing rules for how to adapt loan words into native pronunciation. And sometimes the irregularities or arbitrary parts of that are very interesting.
So personally I'd start with some data. I don't know exactly what theoretical literature there is on this, but there's probably something.
