Cu₂BaGeSe₄ (CBGSe) was previously identified as a potential thin-film photovoltaic (PV) candidate based on computationally scanning the I₂-II-IV-VI₄ (I = Cu, Ag; II = Ba, Sr; IV = Ge, Sn; VI = S, Se) materials family and successful experimental synthesis. This material avoids difficulties of competing PV materials like toxicity (Cd) or scarcity (In, Te) of constituent elements in Cu(In,Ga)(S,Se)₂ and CdTe. Moreover, the similar ionic sizes and coordination preferences compared to the recently identified PV material Cu₂BaSn(S,Se)₄ may provide a potential avenue to overcome the unavoidable antisite disordering that limits the competing material Cu₂ZnSn(S,Se)₄. In this work, hybrid density functional theory (HSE06) including spin-orbit coupling is used to explore the electronic properties of three cation alloying approaches (Ag for Cu, Sr for Ba, and Sn for Ge ) for unalloyed CBGSe, which has a relatively large band gap (1.91 eV). The largest band gap decrease can be achieved by Sn/Ge alloying. The minimum band gap occurs at 1.57 eV for x≈0.70 in alloyed Cu₂BaGe_1-xSn_xSe₄. The minimum occurs just prior to a structural transition from the P3₁ to the Ama2 space group just above x=0.7; the P3₁ phase is associated with a significantly lower band gap.