I went through my translog.txt file and looked at the backpack contents of various types of pets that have been owned by characters I've either transferred across shards or copies to Test Center and this is what I found listed as the kinds of things these pets hold in their backpacks:
Greater Dragons: At least 6 items, always including 4 piles of gems (even if they are identical to each other) and always 2 piles of gold.
Dragons: 3 items, including 2 piles of gems and one pile of gold.
Rune Beetle: 2 to 5 items, including gold, a spell scroll, one or two piles of reagents, a seed. Sometimes they had a small gem, gold, and a seed. One had gold, a spell scroll, and a jaw bone.
Hiryu: Gold.
Bane Dragon: Gold.
Cu sidhe: Gold.
White wyrm: 2 items--gold and 1 pile of gems.
Nightmare: 4 items, including potion bottle, spell scroll, sulfurous ash, gold.
Boura: Commonly up to 2 items (boura pelt and sometimes a boura skin). Do not know if the boura tail shield would show up in the pack of a boura when it becomes tamed.
Fire beetle: 2 items--ingots and sulfurous ash.
Vollem: 4 items, including a potion bottle, spell scroll, sulfurous ash, gold.
My guess is that many of the pets can have bolts and/or arrows in their packs, even if they have died and been rezzed already. (I saw bolts and arrows in the inventories of greater dragons, hiryus, cu sidhe, and nightmares.) I suspect some of them could potentially also have a musical instrument in their backpack. (I found one nightmare I had transferred or copied had a lute in its backpack.)
So if a tamed greater dragon that has never died always has 6 items in its pack and you have 16 of them in the stable, that might count as 16 pets and 96 items (16*6), for a total potential item count of 112 items. However, if they can also pick up bolts and arrows (and some of mine have), you would need to add on another 32 items (16*2), for a total potential item count of 144. If a musical instrument can spawn as greater dragon lute that is preserved in its backpack when it is tamed, tack on 16 more items for a total potential item count of 160.
I don't know how the stabling system actually counts animals and items in their backpacks. However, if it is true that it is just one container, it makes sense to me that the items in the backpacks of stabled pets that have never died probably counts against the item limit for that container. If so, that could be why we have the stable count limit that we do and not something higher. I don't know enough about how containers are handled in UO to know if it would be all that difficult to raise the maximum number of items a stable container could hold, but I would imagine just adding stable slots isn't necessarily as simple as it might sound on the surface.