The Polynomial Modular Number System (PMNS) is a representation system that has shown its effectiveness for finite-field arithmetic with ECC-size integers [4, 7, 9]. Efforts have also been made to adapt it to larger integers [8, 19, 24] with mixed results. In particular in [19], a gap in the 2048-bit to 8192-bit integer sizes was highlighted, for which PMNS seemed incapable of overcoming the competition. In this work, we propose a new way of using PMNS for larger sizes, which involves multi-precision polynomial coefficients and utilizes the Montgomery CIOS reduction, thus closing said gap.