Hoi,
When you see a label in Reasonator, you will find that when it is not in *YOUR* language, it is underlined in red. You can hover over a label and you will be prompted to add a label in the named language. ONLY your language. Wikidata being Wikidata can provide the option as it already does to see multiple labels for the languages as selected in the #Babel template. That is the obvious place to see and edit labels in multiple languages.
When you think that language fallback in Reasonator is "easy", it is very much because the options have been considered properly. It does provide fall back in a user specified manner. It does show all the labels used for an item but it does NOT provide an option to edit them. It could, but this is left for Wikidata itself just like adding statements has been left to Wikidata.
There are three parts to an item in Wikidata. Labels, statements and links. It is best imho not to complicate things and leave this partition in place.
Thanks,
GerardM