The microstructure and mechanical properties of Zr48Cu48 - x Al4M x (M ≡ Fe or Co, x = 0, 0.5, 1 at.%) metallic glass (MG) composites are highly dependent on the amount of Fe or Co added as microalloying elements in the parent Zr48Cu48Al4 material. Addition of Fe and Co promotes the transformation from austenite to martensite during the course of nanoindentation or compression experiments, resulting in an enhancement of plasticity. However, the presence of Fe or Co also reduces the glass forming ability, ultimately causing a worsening of the mechanical properties. Owing to the interplay between these two effects, the compressive plasticity for alloys with x = 0.5 (5.5% in Zr48Cu47.5Al4Co0.5 and 6.2% in Zr48Cu47.5Al4Fe0.5) is considerably larger than for Zr48Cu48Al4 or the alloys with x = 1. Slight variations in the Young's modulus (around 5-10%) and significant changes in the yield stress (up to 25%) are also observed depending on the composition. The different microstructural factors that have an influence on the mechanical behavior of these composites are investigated in detail: (i) co-existence of amorphous and crystalline phases in the as-cast state, (ii) nature of the crystalline phases (austenite versus martensite content), and (iii) propensity for the austenite to undergo a mechanically-driven martensitic transformation during plastic deformation. Evidence for intragranular nanotwins likely generated in the course of the austenite-martensite transformation is provided by transmission electron microscopy. Our results reveal that fine-tuning of the composition of the Zr-Cu-Al-(Fe,Co) system is crucial in order to optimize the mechanical performance of these bulk MG composites, to make them suitable materials for structural applications.