  We focus on several models of modified gravity which share the characteristic
of leading to perturbations of the Newtonian potential $\propto K_2~r^{-2}$ and
$\propto K_3~r^{-3}$. In particular, by using existing long data records of the
LAGEOS satellites, tracked on an almost continuous basis with the Satellite
Laser Ranging (SLR) technique, we set preliminary constraints on the free
parameters $K_2,~K_3$ in a model-independent, phenomenological way. We obtain
$\left|K_2\right|\lesssim 2.1\times 10^6~\textrm{m}^4~\textrm{s}^{-2},~
-2.5\times 10^{12}~\textrm{m}^5~\textrm{s}^{-2}\lesssim K_3 \lesssim 4.1\times
10^{12}~\textrm{m}^5~\textrm{s}^{-2}.$ They are several orders of magnitude
tighter than corresponding bounds existing in the literature inferred with
different techniques and in other astronomical and astrophysical scenarios.
Then, we specialize them to the different parameters characterizing the various
models considered. The availability of SLR data records of increasing length
and accuracy will allow to further refine and strengthen the present results.
