Unlike its classical counterpart, the Seiberg­-Witten equation with multiple spinors does not enjoy a priori estimates which lead to compactness. In fact, compactness can fail; however, in a rather controlled way: after suitable rescaling sequences of solutions of the Seiberg-Witten equation with multiple spinors converge to Fueter sections of a bundle of moduli spaces of ASD instantons. I will give a brief sketch of our proof (based on ideas developed by Taubes for PSL(2,C)-connections). Moreover, I will explain our point of view of the Seiberg- Witten equation within the context of Seiberg-Witten equations with ADHM targets, which will illuminate the connection with gauge theory on G2-manifolds. This is joint work with Andriy Haydys.