  In this paper we investigate whether positive elements in the multiplier
algebras of certain finite C*-algebras can be written as finite linear
combinations of projections with positive coefficients (PCP). Our focus is on
the category of underlying C*-algebras that are separable, simple, with real
rank zero, stable rank one, finitely many extreme traces, and strict comparison
of projections by the traces. We prove that the strict comparison of
projections holds also in the multiplier algebra of the stabilizer algebra.
Based on this result and under the additional hypothesis that the multiplier
algebra has real rank zero, we characterize which positive elements of the
multiplier algebra are PCP.
