High-resolution neutral hydrogen (HI) observations undertaken over the past decade have revealed the morphology and kinematics of spiral galaxies in elaborate detail. These observations hint at the existence of extended, diffuse components associated with filaments seen to extend from the disk in certain galaxies. The full extent of such features is invisible to interferometers due to the inherent lack of sensitivity at the largest angular scales. The origin of these features also remains unclear. Do they originate from stellar outflows, interactions with companions, or accrete from the intergalactic medium as simulations suggest? Large single dishes possess superior surface brightness and angular sensitivity to accurately capture the full extent of anomalous HI structures seen around nearby galaxies. I present initial results from the first systematic study of deep (N$_{HI}$~10$^{18}$ cm$^{-2}$) observations of the HALOGAS survey performed with the Robert C. Byrd Green Bank Telescope (GBT). These GBT data reveal, on average, 10% more HI than the original WSRT observations in the form of large, diffuse HI reservoirs, which likely trace large amounts of ionized gas. The morphology of this excess HI is similar to what one would expect theorized cold flows to take in emission. Additionally, the excess HI traces anomalous features seen in the high-resolution observations both spectrally and spatially. The foundational work we present in this study provides a starting point to relate the overall HI environment to intrinsic galaxy properties known to be responsible for extraplanar gas in galaxies. The application of the methods outlined in this work to the full HALOGAS sample, which covers a wide range of galaxy environment properties, will provide insight into the origins of the many large HI filaments seen around nearby galaxies. I will also present results from early commissioning observations performed with a cryogenic phased array feed (PAF) for the GBT. This instrument will increase survey speeds by a factor of 3-5 by forming multiple beams on the sky, and will be the first such instrument in full-time use on a large single dish in the world.