Can’t believe I missed this thread! Well we tested a POC development recently with that exact problem. It was a POC so no requirements or acceptance criteria , just a business brief of what type of product we wanted to trial to see if we could utilise the data we alrady had domain knowledge on.
So I searched the club for a techniques and found What tools and things do you use to help you with exploratory software testing? - #52 by thomjr . So rather than seeing it as testing, we saw it as a feedback loop and used the PQIP technique so that testers could use their intuition, but to give the product, design and dev teams insight. The whole test spent an hour reviewing the POC and documenting on confluence using a PQIP grid. That really worked.
Now if you have a productionised product feature your testing that has a lack of clear requirements, then I think PQIP would still work - just the feedback loops need to be quicker.