  This paper introduces a novel class of PICOD($t$) problems referred to as
$g$-group complete-$S$ PICOD($t$) problems. It constructs a multi-stage
achievability scheme to generate pliable index codes for group complete PICOD
problems when $S = \{s\}$ is a singleton set. Using the maximum acyclic induced
subgraph bound, lower bounds on the broadcast rate are derived for singleton
$S$, which establishes the optimality of the achievability scheme for a range
of values for $t$ and for any $g$ and $s$. For all other values, it is shown
that the achievability scheme is optimal among the restricted class of
broadcast codes.
