That would be an awesome product (do a Kickstarter! lol), but afaik it doesn't currently exist. I use two things instead: an immersion (stick) blender & a motorized stirring arm. The stick blender is great for stuff like soups or applesauce or whatever, anything that you want to puree in the bowl itself. I have a Miallegro, which is no longer sold unfortunately:
https://www.amazon.com/Miallegro-9080-Immersion-Stainless-Attachment/dp/B00275T6YC/
Aside from being stupid powerful, it also came with a bunch of attachments that mimic'd some functions of a food processor, as well as a single whisk, which could simulate a mixer for certain purposes. Plus it had a nice little vertical cup, which is super useful for homemade mayo (takes about 30 seconds!). Poke around Amazon for immersion blenders that come with accessories, like this one:
https://www.amazon.com/Immersion-Processor-Smoothies-Puree-Heavy-Stainless/dp/B071RB7WWS
The other unit I use is the Gourmia GST210R robot pot stirrer. $30 on Amazon:
https://www.amazon.com/Gourmia-GST210R-Stiriffic-Adjustable-Automatic/dp/B01GSLYSRK
It is cheap-feeling & has funky battery requirements (you have to charge it for 24 hours initially, and FULLY discharge it before recharging it again), but it does the job. I've tested it on the 3qt Mini IP and the regular 6qt IP and it works fine. It's great for anything that requires constantly stirring like a gravy, risotto, custard ice cream base, etc.
Otherwise, probably your best bet is just to find an electric hand mixer with slightly longer-than-normal beaters to fit in the IP bowl.