I often go and plant my own stuff on village fields - both using their plots and making my own next to theirs. In my experience the key is to not get caught, you can't let people see you picking stuff up. They don't seem to mind you extending their fields. So you harvest during the night, so those annoying maidens wandering around don't spot you in the act of pulling some turnips out. Another thing is, when harvest time comes, I'm pretty sure the villagers will harvest your plots for themselves along with theirs, but they can't harvest all of them at once and there will still be plenty of unharvested ones for a while after harvest season starts.
Pretty sure they make no distinction between their plots and the ones you made next to theirs, they're all considered to be theirs and you'll get a warning and then a good beating if spotted.
After harvesting just pile the goods in some safe spot nearby, recently there was a feature added where villagers get suspicious if they see you hauling a lot of veggies in the village that look like they're from their field... Later on when everyone's gone to sleep, I'm loading the pile onto my bull and heading home with a self-satified feel of a job well done.
The stuff they harvested "for me" will be in their shops and stores, which is useful to me because in late game you usually have plenty of stuff to trade with. Piles of turnips and wheat can be had for cheap, those piles would've taken a lot of time and back-breaking effort to harvest on a private field.