Actually the 3 discs used in the street triple are lighter combined then 2 discs used in the dual. Our triples work in the stock bell housing.
Understanding how the clutch works is the key to a fast shifting clutch. Meaning when you push your clutch pedal in, the release bearing moves the clutch fingers around 1/2" letting the pressure plate that holds pressure on the disc to move back about 0.050",creating a gap. Everything in front of the pressure plate "disc's and floaters" must slide apart easily.
If anyone of those hang up the clutch will not shift correctly. We take each disc prior to installation and slide them on and off the splines on the input shaft. If they hesitate we debur with a file. We also use graphite on the splines to make them slide like butter, and the graphite doesn't attracted dirt like grease does. Also not burring them all up when stabbing the transmission is also important, take your time when stabbing it and never pull in in by the bolts. The alignment tool should pull in and out very easy prior to install, or the disc's are not lined up correctly.