We present a systematic study mapping how the As incorporation into GaAsySb1-y and AlxGa1-xAsySb1-y (y < 0.2) grown by molecular beam epitaxy under Sb overpressure varies under different growth conditions. GaAsSb epilayers were grown on GaSb substrates with different As fluxes, growth rates, and substrate temperatures. X-ray diffraction was used to determine the As mole fraction in the samples. The As mole fraction when growing GaAsSb in Sb overpressure was found to (i) be much less sensitive to unwanted variations in the Sb flux as compared to growing in Sb underpressure (i.e. with Sb/III Aux ratio less than unity), (ii) increase with increasing As flux, (iii) increase with increasing substrate temperature, and (iv) increase with decreasing Ga flux. AlGaAsSb epilayers with different Al mole fractions were also grown. No enhancement in the As incorporation due to Al was found for these growth conditions.