Electrocatalyst discovery is an inherently multiobjective challenge that can benefit from closed-loop approaches towards acceleration. However, previous computational closed-loop efforts for electrocatalysis often focus on a single objective to be optimized. Here we demonstrate a multiobjective closed-loop strategy towards identifying single-atom alloy (SAA) electrocatalysts for nitrogen reduction considering activity, stability, and cost. Candidates were autonomously selected via a multiobjective scoring approach, as implemented in our AutoCat software, and evaluated using a high-throughput density functional theory pipeline. We discuss the implications of our scoring system formulation and show its ability to efficiently explore the SAA design space. We also propose a multiobjective method to rank evaluated candidates balancing the three target metrics, with Zr$_1$Cr, Hf$_1$Cr, Ag$_1$Re, Au$_1$Re, and Ti$_1$Fe ranking the highest. The inclusion of Hf is of particular interest as it is more commonly found within the context of molecular catalysts, which are similar yet distinct from SAAs.