  We present forecasted cosmological constraints from combined measurements of
galaxy cluster abundances from the Simons Observatory and galaxy clustering
from a DESI-like experiment on two well-studied modified gravity models, the
chameleon-screened $f(R)$ Hu-Sawicki model and the nDGP braneworld Vainshtein
model.
  A Fisher analysis is conducted using $\sigma_8$ constraints derived from
thermal Sunyaev-Zel'dovich (tSZ) selected galaxy clusters, as well as linear
and mildly non-linear redshift-space 2-point galaxy correlation functions. We
find that the cluster abundances drive the constraints on the nDGP model while
$f(R)$ constraints are led by galaxy clustering. The two tracers of the
cosmological gravitational field are found to be complementary, and their
combination significantly improves constraints on the $f(R)$ in particular in
comparison to each individual tracer alone.
  For a fiducial model of $f(R)$ with $\text{log}_{10}(f_{R0})=-6$ and $n=1$ we
find combined constraints of $\sigma(\text{log}_{10}(f_{R0}))=0.48$ and
$\sigma(n)=2.3$, while for the nDGP model with $n_{\text{nDGP}}=1$ we find
$\sigma(n_{\text{nDGP}})=0.087$. Around a fiducial General Relativity (GR)
model, we find a $95\%$ confidence upper limit on $f(R)$ of
$f_{R0}\leq5.68\times 10^{-7}$. Our results present the exciting potential to
utilize upcoming galaxy and CMB survey data available in the near future to
discern and/or constrain cosmic deviations from GR.
