  We carry out a multi-probe self-consistency test of the flat $\Lambda$CDM
model with the aim of exploring potential causes of the reported tensions
between high- and low-redshift cosmological observations. We divide the model
into two theory regimes determined by the smooth background (geometry) and the
evolution of matter density fluctuations (growth), each governed by an
independent set of Lambda Cold Dark Matter ($\Lambda$CDM) cosmological
parameters. This extended model is constrained by a combination of weak
gravitational lensing measurements from the Kilo-Degree Survey, galaxy
clustering signatures extracted from Sloan Digital Sky Survey campaigns and the
Six-Degree Field Galaxy Survey, and the angular baryon acoustic scale and the
primordial scalar fluctuation power spectrum measured in $\textit{Planck}$
cosmic microwave background (CMB) data. We find strong consistency between the
geometry and growth parameters, and with the posterior of standard $\Lambda$CDM
analysis. Tension in the amplitude of matter density fluctuations as measured
by the parameter $S_8$ persists at around 3$\sigma$, with a $1.5\,\%$
constraint of $S_8 = 0.776_{-0.008}^{+0.016}$ for the combined probes. We also
observe a less significant preference (at least $2\sigma$) for higher values of
the Hubble constant, $H_0 = 70.5^{+0.7}_{-1.5}\,{\rm km\, s^{-1} Mpc^{-1}}$, as
well as for lower values of the total matter density parameter $\Omega_{\rm{m}}
= 0.289^{+0.007}_{-0.005}$ compared to the full $\textit{Planck}$ analysis.
Including the subset of the CMB information in the probe combination enhances
these differences rather than alleviate them, which we link to the discrepancy
between low and high multipoles in $\textit{Planck}$ data.
