We present the analysis of the diffuse, low column density HI environment of 18 MHONGOOSE galaxies. We obtained deep observations with the Robert C. Byrd Green Bank Telescope, and reached down to a 3sigma column density detection limit of NHI=6.3x10^{17} cm^{-2} over a 20 km/s linewidth. We analyze the environment around these galaxies, with a focus on HI gas that reaches column densities below NHI=10^{19} cm^{-2}. We calculate the total amount of HI gas in and around the galaxies revealing that nearly all of these galaxies contained excess HI outside of their disks. We quantify the amount of diffuse gas in the maps of each galaxy, defined by HI gas with column densities below 10^{19} cm^{-2}, and find a large spread in percentages of diffuse gas. However, by binning the percentage of diffuse HI into quarters, we find that the bin with the largest number of galaxies is the lowest quartile (0-25% diffuse HI). We identified several galaxies which may be undergoing gas accretion onto the galaxy disk using multiple methods of analysis, including azimuthally averaging column densities beyond the disk, and identifying structure within our integrated intensity (Moment 0) maps. We measured HI mass outside the disks of most of our galaxies, with rising cumulative flux even at large radii. We also find a strong correlation between the fraction of diffuse gas in a galaxy and its baryonic mass, and test this correlation using both Spearman and Pearson correlation coefficients. We see evidence of a dark matter halo mass threshold of M_{halo}~10^{11.1} msun{} in which galaxies with high fractions of diffuse HI all reside below. It is in this regime in which cold-mode accretion should dominate. Finally, we suggest a rotation velocity of v_{rot}~80 kms as an upper threshold to find diffuse gas-dominated galaxies.
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