Poly(isoprene-b-styrene-b-ethylene oxide) (ISO) triblock copolymers were blended with poly(styrene) and poly(isoprene) homopolymers at compositions close to those previously shown to produce triply periodic, multiply continuous network phases. Homopolymer molecular weights were approximately equal to the corresponding block molecular weights, and homopolymer concentrations up to 21 vol % were explored without evidence of phase separation. Three triply periodic network phases were identified: a core-shell double gyroid (Q(230), Ia (3) over bard space group symmetry), an orthorhombic network (O-70, Fddd space group symmetry), and an alternating gyroid (Q(214), I4(1)32 space group symmetry). Tuning the overall composition by adding homopolymer resulted in systematic phase transitions between the Q(230) and O-70 networks and between the Q(214) and O-70 networks. In addition, doping with both poly(styrene) and poly(isoprene) homopolymer induced transitions from three-domain lamellae (LAM(3)) to the O-70 network phase. In general, phases identified in the triblock/homopolymer systems are located at nearly the same compositions established for undiluted ISO. Specific structural assignments and qualitative assessments of long-range order were made using small-angle X-ray scattering (SAXS), birefringence, dynamic mechanical spectroscopy (DMS), and transmission electron microscopy (TEM) data acquired from polydomain (powdered) samples. The results presented herein demonstrate an efficient method for exploring triblock copolymer phase space based on precise and continuous composition control.