I've been trading my excess meat at villages. My usual routine is to load 300 cuts on my small cow. Many times now I've carried 300 over to the cow, dropped it and pushed the 300 cuts onto the cow. Once done, it has divided the 300 into two stacks on the cow, roughly 245 and 55. No problem, so far.

However, I've found, several times, that when the cow is holding almost her max number of different items my cow receives the larger stack but not the smaller stack, and that the original stack of 300 is still whole.