When I want to say there are a number of farmers who are owning a number of cows respectively, without knowing how many cows each farmer is owning, does the phrase
farmers' cows
accurately reflect my intention?
(The) farmers' cows does mean the cows of more than one farmer.
If you really wish to indicate that a number of farmers own a number of cows than you will have to say 'A number of farmers own a number of cows'.