In this article, we derive sufficient conditions for the existence of countably infinitely many positive solutions for an iterative system of higher order singular Rimean- Liouville(R-L) fractional order boundary value problems with Riemann–Stieltjes(R-S) integral boundary conditions involving increasing homeomorphism and positive homomorphism operator(IHPHO) by applying Hölder’s inequality and Krasnoselskii’s cone fixed point theorem in a Banach space. Also, we derive sufficient conditions for the uniqueness of the solution for the problem by fixed point theorem on a complete metric space.