Can Purifi's SPK5 be improved with a passive radiator?

[RickS]

Would two side PR be advantageous for getting a kind of cardiod bass/midrange or am I now too optimistic and is at the back the best location and why?

I do not have much experience with cardioid design, but have studied Linkwitz’s work and so would suggest you check into it as well. For the Purifi designs, I am not aware of any attempt to create a cardioid response. The placement of the passive radiators appears more of a cabinet design choice. This is the case for Directiva as well.

From what I have studied, getting a cardioid response is going to require more active drivers than passive ones. If you look at the primary SPL output from a passive radiator, its contribution is below 100 Hz. So really not able to influence midrange radiation pattern much.