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We numerically and analytically work out the first-order post-Newtonian (1pN)orbital effects induced on the semimajor axis $a$, the eccentricity $e$, theinclination $I$, the longitude of the ascending node $\Omega$, the longitude ofperihelion $\varpi$, and the mean longitude at epoch $\epsilon$ of a testparticle orbiting its primary, assumed static and spherically symmetric, by adistant massive third body X. For Mercury, the rates of change of the lineartrends found are $\dot I_\mathrm{1pN}^\mathrm{X} =-4.3\,\mathrm{microarcseconds\,per\,century}\,\left(\mu\mathrm{as\,cty}^{-1}\right)$,$\dot\Omega_\mathrm{1pN}^\mathrm{X} = 18.2\,\mu\mathrm{as\,cty}^{-1}$,$\dot\varpi_\mathrm{1pN}^\mathrm{X} = 30.4\,\mu\mathrm{as\,cty}^{-1}$,$\dot\epsilon_\mathrm{1pN}^\mathrm{X} = 271.4\,\mu\mathrm{as\,cty}^{-1}$,respectively. Such values, which are due to the added actions of the otherplanets from Venus to Saturn, are essentially at the same level of, or largerby one order of magnitude than, the latest formal errors in the Hermean orbitalprecessions calculated with the EPM2017 ephemerides. The perihelion precession$\dot\varpi_\mathrm{1pN}^\mathrm{X}$ turns out to be smaller than some valuesrecently appeared in the literature in view of a possible measurement with theongoing BepiColombo mission. Linear combinations of the supplementary advancesof the Keplerian orbital elements for several planets, if determinedexperimentally by the astronomers, could be set up in order to disentangle the1pN $N$-body effects of interest from the competing larger precessions likethose due to the Sun's quadrupole moment $J_2$ and angular momentum$\boldsymbol{S}$.

New general relativistic contributions to Mercury's orbital elements and their measurability