A general phenomenological model is presented that predicts the evolution of magnetic order and transition temperatures found in binary noble metal (NM) alloys with high Mn content. The model is derived from magnetic measurements and analysis of rapidly solidified Ag1-xMnx (0.25 <= x <= 0.4) alloys, also describing the magnetic attributes of CuMn and AuMn alloys, as reported in the literature. Mn atomic substitution in the face-centered-cubic noble metal lattice results in a tunable average Mn-Mn characteristic interatomic distance estimated from the average Mn concentration that governs the evolution of the magnetic ordering temperature. This evolution is found to be a consequence of the competition between positive ferromagnetic (FM) and negative antiferromagnetic (AF) interatomic exchange coupling revealing a Bethe-Slater-type behavior. Considering the composition range analyzed in this letter and the previous literature (x = 0.02-0.40), the ordering temperature is maximized at x approximate to 0.17 for Ag-Mn and Cu-Mn alloys, with a progressive decrease at higher Mn concentration that is indicative of an increasing AF character. These predictive results enable the development of potential pathways to manipulate and tailor magnetic attributes in Mn-based alloys that are of current interest for tunable exchange-biased systems.