Neural Radiance Fields (NeRFs) have unmatched fidelity on large, real-world scenes. A common approach for scaling NeRFs is to partition the scene into regions, each of which is assigned its own parameters. When implemented naively, such an approach is limited by poor test-time scaling and inconsistent appearance and geometry. We instead propose InterNeRF, a novel architecture for rendering a target view using a subset of the model's parameters. Our approach enables out-of-core training and rendering, increasing total model capacity with only a modest increase to training time. We demonstrate significant improvements in multi-room scenes while remaining competitive on standard benchmarks.