I did some searching on line and came across several distributors of a "4 in 1 multifunction" (color) pen kit. All seem to be the same design (like the PSI), most likely the same manufacturer. The reviews I read were a mixed bag.
Gimmicky IMO.
It would be something if you could reengineer the bic version as it uses 4 different click to expose mechanisms. Unlike the PSI version which requires the pen to be held horizontal and then rotated for gravity to choose a color. Hence I believe the issues with the design.
I would rather carry one of the two color pen kits and a mechanical pencil. That way you have the multi colors that most would want, Blue or Black and red and then the pencil function, made from the same blank. Less hassle with the mechanisms and achieve the same end goal. Just my opinion.