The aim of this work was to design and optimize compositions of three-component composites based on polyetheretherketone (PEEK) with enhanced tribological and mechanical properties. Initially, two-component PEEK-based composites loaded with molybdenum disulfide (MoS2) and polytetrafluoroethylene (PTFE) were investigated. It was shown that an increase in dry friction mode tribological characteristics in metal-polymer and ceramic-polymer tribological contacts was attained by loading with lubricant fluoroplastic particles. In addition, molybdenum disulfide homogenized permolecular structure and improved matrix strength properties. After that, a methodology for identifying composition of multicomponent PEEK-based composites having prescribed properties which based on a limited amount of experimental data was proposed and implemented. It was shown that wear rate of the “PEEK + 10% PTFE + 0.5% MoS2” composite decreased by 39 times when tested on the metal counterpart, and 15 times on the ceramic one compared with neat PEEK. However, in absolute terms, wear rate of the three-component composite on the metal counterpart was 1.5 times higher than on the ceramic one. A three-fold increase in wear resistance during friction on both the metal and ceramic counterparts was achieved for the “PEEK + 10% PTFE + 0.5% MoS2” three-component composite compared with the “PEEK + 10% PTFE”. Simultaneous loading with two types of fillers slightly deteriorated the polymer composite structure compared with neat PEEK. However, wear rate was many times reduced due to facilitation of transfer film formation. For this reason, there was no microabrasive wear on both metal and ceramic counterpart surfaces.