  We study unary parts of centraliser clones on the set $\{0,1,2,3\}$,
so-called centralising monoids. We describe and count all centralising monoids
on the set $\{0,1,2,3\}$ having majority operations as witnesses, and we list
the inclusion maximal proper submonoids of the full transformation monoid among
them. This extends previous work by Goldstern, Machida and Rosenberg.
