Abstract: Fountain used cancellative monoids and bisystems of cancellative monoids to construct PA blocked Rees matrix semigroups, the structure of which extended Rees matrix semigroups over cancellative monoids. We construct PCA blocked Rees matrix semigroups by -monoids and bisystems of -monoids. PA blocked Rees matrix semigroups are PCA blocked Rees matrix semigroups. An example is given to illustrate a semigroup can be a PCA blocked Rees matrix semigroup but not a PA blocked Rees matrix semigroup.