It is quite possible to have users submit several categories simultaneously in a modify form. But having them submit many categories is not better than having them submit only one!
What we need to do is have users submit zero categories in a modify form. It is an absolute requirement that the modify form should return no categories at all -- not multiple categories, no categories. The link that is being modified already has categories which must not be changed by the user in any circumstances.
The solution is simply to allow users to modify links without affecting the categories, just like the other columns which they may not alter.
What prevents them? Nothing much -- just a bit of code somewhere that rejects a modify form if there is no category input field -- but we can't find that bit of code.