  Utilizing the well-established Radial Tully-Fisher (RTF) relation observed in
a `large' (843) sample of local galaxies, we report the maximum allowed
variance in the Hubble parameter, $H_0$. We estimate the total intrinsic
scatter in the magnitude of the RTF relation(s) implementing a cosmological
model-independent cosmographic expansion. We find that the maximum allowed
local variation in our baseline analysis, using 4 RTF relations in the galaxy
sample is $\Delta H_0/H_0 \lesssim 3 \%$ at a $95\%$ C.L. significance. Which
is implied form a constraint of $\Delta H_0/H_0 = 0.54^{+1.32}_{-1.37} \%$
estimated at $D_{\rm{L}}\sim 10\, [\rm{Mpc}]$. Using only one
`best-constrained' radial bin we report a conservative $95\%$ C.L. limit of
$\Delta H_0/H_0 \lesssim 4 \%$. Through our estimate of maximum variation, we
propose a novel method to validate several late-time/local modifications put
forth to alleviate the $H_0$ tension. We find that within the range of the
current galaxy sample redshift distribution $10 \, [\rm{Mpc}] \le D_{\rm{L}}
\le 140\, [\rm{Mpc}]$, it is highly unlikely to obtain a variation of $\Delta
H_0/H_0 \sim 9\%$, necessary to alleviate the $H_0$-tension. However, we also
elaborate on the possible alternative inferences when the innermost radial bin
is included in the analysis. Alongside the primary analysis of fitting the
individual RTF relations independently, we propose and perform a joint analysis
of the RTF relations useful to create a pseudo-standardizable sample of
galaxies. We also test for the spatial variation of $H_0$, finding that the
current samples' galaxies distributed only in the southern hemisphere support
the null hypothesis of isotropy, within the allowed noise levels.
