Brain-Computer Interfaces (BCI) are an interesting emerging technology that is driven by the motivation to develop an effective communication interface translating human intentions into a control signal for devices like computers or neuroprostheses. If this can be done bypassing the usual human output pathways like peripheral nerves and muscles it can ultimately become a valuable tool for paralyzed patients. Most activity in BCI research is devoted to finding suitable features and algorithms to increase information transfer rates (ITRs). The present paper studies the implications of using more classes, e.g., left vs. right hand vs. foot, for operating a BCI. We contribute by (1) a theoretical study showing under some mild assumptions that it is practically not useful to employ more than three or four classes, (2) two extensions of the common spatial pattern (CSP) algorithm, one interestingly based on simultaneous diagonalization, and (3) controlled EEG experiments that underline our ...