We demonstrate a marked increase in the possible growth domain and growth rate of the O plasma-assisted molecular beam epitaxy of β-(Al x Ga 1− x ) 2 O 3 , by adding the element In during growth. We explain these enhancement results from a metal-exchange catalytic effect. This mechanism allows us to synthesize β-(Al x Ga 1− x ) 2 O 3 /β-Ga 2 O 3 heterostructures at growth conditions that are not accessible in the absence of In, stabilizing the monoclinic β-phase. We demonstrate the growth of β-(Al x Ga 1− x ) 2 O 3 at growth temperatures up to 900 °C. Moreover, we illustrate how additional In on the β-(Al x Ga 1− x ) 2 O 3 surface acts as a surface active agent, improving the crystal quality of the synthesized β-(Al x Ga 1− x ) 2 O 3 /β-Ga 2 O 3 heterostructures. These structures are shown to be of the highest crystal quality up to an Al concentration of x = 0.2. We predict the novel growth mode introduced for ternary III–O thin film synthesis — shown by the example of β-(Al x Ga 1− x ) 2 O 3 — to be applicable for a wide range of thin film materials, whose individual constituents possess material properties similar to those discussed for the constituents contributing to β-(Al x Ga 1− x ) 2 O 3 .