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Non-spherical systems described by MOND theories of modified gravity arisingfrom generalizations of the Poisson equations are affected by a MONDianextra-quadrupolar potential \phi_M even if they are isolated and they are indeep Newtonian regime. In general MOND theories quickly approaching Newtoniandynamics for accelerations beyond A_0, \phi_M is proportional to amultiplicative scaling coefficient \alpha \sim 1, while in MOND models becomingNewtonian beyond \kappa A_0, \kappa >> 1, it is enhanced by \kappa^2. Weanalytically work out some orbital effects due to \phi_M in the framework ofQUMOND, and compare them with the latest observational determinations of SolarSystem's planetary dynamics, exoplanets and double lined spectroscopic binarystars. The current admissible range for the anomalous perihelion precession ofSaturn yields |\kappa| <= 3.5 x 10^3, while the radial velocity of \alpha CenAB allows to infer |\kappa|<= 6.2 x 10^4 (A) and |\kappa|<= 4.2 x 10^4 (B). Inevaluating such preliminary constraints it must be recalled that QUMOND is notthe nonrelativistic limit of TeVeS.

Constraints on a MOND effect for isolated aspherical systems in deep Newtonian regime from orbital motions