  Recently it was suggested that the neutrino may violate the Pauli exclusion
Principle (PEP). This renews interest in the systematic search for bilinear
commutation relations that could describe deviations from PEP. In the context
of this search we prove a no-go theorem which forbids a finite occupancy limit
for an arbitrary system with a bilinear commutation relation. In other words,
either the upper limit on the occupancy number is 1 (the ordinary fermionic
case) or there is no upper limit at all. Some examples of the latter class
include the usual Bose statistics, as well as non-standard quon statistics and
infinite statistics.
