Thin films of immiscible polymer blends will undergo phase separation into large domains, but this behavior can be suppressed with additives that accumulate and adhere at the polymer/polymer interface. Herein, we describe the phase behavior of polystyrene/poly(methyl methacrylate) (PS/PMMA) blends with 20 vol % of a bottlebrush additive, where the bottlebrush has poly(styrene-r-methyl methacrylate) side chains with 61 mol % styrene. All blends are cast into films and thermally annealed above the glass transition temperature. The phase-separated structures are measured as a function of time with atomic force microscopy and optical microscopy. We demonstrate that subtle changes in bottlebrush architecture and homopolymer chain lengths can have a large impact on phase behavior, domain coarsening, and domain continuity. The bottlebrush additives are miscible with PS under a broad range of conditions. However, these additives are only miscible with PMMA when the bottlebrush backbones are short or when the PMMA chains are similar in length to the bottlebrush side chains. Otherwise, the limited bottlebrush/PMMA miscibility drives the formation of a bottlebrush-rich interphase that encapsulates the PMMA-rich domains, stabilizing the blend against further coarsening at elevated temperatures. The encapsulated domains are aggregated in short chains or larger networks, depending on the blend composition. Interestingly, the network structures can provide continuity in the minor phases.