Adsorption of the two oxyanions, arsenate (As(V)) and arsenite (As(III)), on a common goethite-based granular porous adsorbent is studied in the presence of major co-existing ions in groundwater (i.e., phosphate, silicic acid, sulfate, carbonate, magnesium, and calcium) and predicted using the extended triple layer model (ETLM), a dipole modified single-site triple layer surface complexation model consistent with spectroscopic and molecular evidence. Surface species of all ions were selected according to the previous ETLM studies and published experimental spectroscopic/theoretical molecular information. The adsorption equilibrium constants for all ions were determined using adsorption data obtained in single-solute systems. The adsorption equilibrium constants referenced to the site-occupancy standard state (indicated by Kθ) were compared with those for goethite in the literature if available. The values of these constants for the goethite-based adsorbent are found to be close to the values for goethite previously studied. These “constrained” adsorption equilibrium constants determined in single-solute systems were used in the ETLM to predict the competitive interactions of As(III, V) with the co-existing ions in binary-solute systems. The ETLM is capable of predicting As(III, V) adsorption in the presence of oxyanions (phosphate, silicic acid, sulfate, and carbonate). This study presents the first successful and systematic prediction of the competitive interactions of As(III, V) with these oxyanions using the ETLM. The ETLM prediction of surface (and aqueous) speciation also provides insights into the distinct adsorption behavior of As(III, V) in the presence of the oxyanions. Magnesium and calcium significantly enhanced As(V) adsorption at higher pH values, while they had little effect on As(III) adsorption. The enhanced adsorption of As(V), however, could not be predicted by the ETLM using the surface species proposed in previous ETLM studies. Further studies are necessary to identify ternary complexes, especially at high pH. Adsorption isotherms of As(V), a dominant form of arsenic in adsorptive water treatment systems, in the presence of the co-existing ions under relevant conditions of water treatment systems are also obtained and predicted by the ETLM to study and compare the effect of the co-existing ions on As(V) removal.