Previous work has identified the importance of the lipophilic-fluorophilic block length ratio R-1 in predicting the morphology of linear lipophilic-hydrophilic-fluorophilic (hereafter referred to as BAC) micelle systems. Here, a generalized form R of this structural parameter is developed that makes no assumption of BAC triblock co-polymer linearity, while still providing accurate predictions of the micelle morphology. The morphologies of BAC micelles formed by triblock co-polymers with R << 1 or R >> 1 have similar features, with the only notable difference being an inversion of the lipophilic and fluorophilic regions. A destabilization of the single-core micelle structure occurs as R approaches unity from either direction. Finally, the extent to which the micelle morphology depends on the polymer architecture instead of the composition alone is examined, with a decreased patchiness observed in BAC systems with very long block lengths. Through the modification of both the R-value and the polymer architecture, the micelle morphology can be effectively tuned for use in immobilized catalysis and nanoreactor applications.