Introducing an interaction parameter γ, we implement modifier interaction and the mixed-alkali effect into bond constraint theory, and apply this extension for simplistic property prediction on ternary phosphate glasses. The severity of the mixed alkali effect results from the interplay of two simultaneous contributions: Bond constraints on the modifier species soften or stiffen with decreasing or increasing γ, respectively. When the modifier size is not too dissimilar the decrease in γ reflects that the alkali ions can easily migrate between different sites, forcing the network to continuously re-accommodate for any subsequent distortions. With increasing size difference, migration becomes increasingly difficult without considerable network deformation. This holds even for smaller ions, where the sluggish dynamics of the larger constituent result in blocking of the fast ion movement, leading to the subsequent increase in γ. Beyond a certain size difference in the modifier pair, a value of γ exceeding unity may indicate the presence of steric hindrance due to the large surrounding modifiers impeding the phosphate network to re-accommodate deformation.