What is a white cap, and how did it get into your combine hopper to start with?
IMO, a white cap is a kernel or even multiple kernels of wheat still attached to the glume and often a small piece of stem, usually the tip or end of the head of wheat.
IMO, the head of wheat hits a high speed threshing device and very quickly the head is broken into pieces in attempts to get the grain kernels out of the glume and seperate them from the stems and other chaff. If the tip of the wheat head is broken away from the rest of the head instantly upon contact with the high speed threshing device, it can still be threshed if it can be contained within the threshing mechanism long enough. However, if there is no means, or not enough means to keep that portion of the wheat head in the threshing mechanism long enough to be threshed, then it can be released to the cleaning mechanism in tact.
IMO once in the cleaning mechanism, no further means of efficient threshing are available. Rethreshers are not nearly as efficient as the main threshing mechanism. Once the unthreshed portion of the wheat head has entered the cleaning mechanism, it can either continue on through and be released to the ground, or it can be allowed into the combine hopper. That is the choice the operator makes when setting the clearences and air speed of the cleaning unit.
So, IMO, it is best to install a means to contain all parts of the wheat head in the threshing mechanism untill it is completely threshed. Only way I know of that is bolt on is a cover plate setup for the concave. Some also use a clip on product known as "interuptors". This product, which I have zero personal experience with, is supposed to be installed between the welded crossbars of the concave and act as a crossbar space filler. This is supposed to serve two purposes. One is to greatly decrease the amount of space between crossbars where the white cap can fall through. The other is to reduce the material retardation throughout that part of the concave by not allowing the material to deflect between the crossbars and become held there for a slit second.
For my theories of dealing with unthreshed head pieces, I choose the cover plates for the outside of the concave. This leaves the crossbar dimensions alone which allow for greater threshing abilities, but is a means of keeping the unthreshed wheat head parts in the threshing mechanism for a greater period of time. Hopefully long enough for the kernels to become seperated from the glume and stem pieces.
Increasing the aggression of the threshing mechanism by installing larger more aggressive rasp bars, is really only helpfull if you have limited means of containment. Rather if you only have one cover plate, or the seperation unit is compromised too much by installing more covers over the threshing mechanism, then more threshing needs to be done in a shorter distance in the threshing mechanism.