We report on the characterization of the morphological behavior expressed between the symmetric AB diblock and ABC triblock copolymer states. Experimentally, a gradual transformation between these states was achieved through systematic addition of PEO to a single symmetric PS-PI diblock copolymer (MW similar to 18 800 g/mol), resulting in a series of 10 poly(styrene-b-isoprene-b-ethylene oxide) triblock copolymers varying only in the amount of PEO added. Final compositions ranged from 2.9 to 33.2 vol % (experimentally symmetric) PEO, with the remaining volume necessarily divided equally between the PS and PI segments. The molecular weight of the parent diblock was chosen such that resulting triblocks would undergo order-disorder transitions (ODTs) at experimentally accessible temperatures over much of the composition range studied. Our results focus on the detection and characterization of six morphologies observed to form between these two symmetric states and some of the kinetic and directional (heating vs cooling) characteristics of two thermally induced order-order transitions (OOTs) observed. We conclusively identify the formation of two- and three-domain lamellar structures, hexagonally packed core-shell cylinders, and the pentacontinuous core-shell gyroid morphology and speculate on probable assignments for two untypical structures also observed. Finally, we discuss some of the general behavior characteristics of this system in terms of their dependence on block connectivity and chi interaction parameter sequencing.