Zr70–76Al7–7.5Ni13–15Cu2Ag2–5 glassy alloys were prepared by melt-spinning with Zr contents up to 76 at.%, greatly exceeding the highest Zr content of 70 at.% previously reported for Zr-based glassy alloys exhibiting a calorimetric glass transition. The 70–72Zr and 74Zr alloys were also cast as bulk rods up to 1.5 mm in diameter with glass and [glass + β-Zr + ω-Zr] phases, respectively, by ejection copper-mold casting. The crystallization temperature and Vickers hardness Hv for the glassy ribbons decrease with increasing Zr content from 70 to 76 at.%. The glassy rods show high yield strength (σy) of 1225–1346 MPa, high fracture strength (σf) of 1497–1499 MPa, and large compressive plastic strain (εp) of 9.7–3.2% for the 70–72Zr alloys. Similarly, the 74Zr rod with [glass + β-Zr + ω-Zr] phases shows σy of 1325 MPa, σf of 1472 MPa, εp of 2.4%. The 76Zr thick ribbon with [glass + β-Zr + ω-Zr] phases shows, in tension, high σy of 890 MPa, σf of 988 MPa, and plastic elongation of 0.3%. The Zr-rich glassy ribbons crystallize, showing three exothermic peaks upon heating. The first-stage peak is due to the precipitation of icosahedral quasicrystal (IQ) for the 70–72Zr ribbons, and β-Zr + ω-Zr for the 74–76Zr ribbons. These annealing-induced mixed-phase ribbons with Zr content above 72 at.% exhibit good bending plasticity, even though their HV is about 41% higher than for the as-spun glassy ribbons. Similarly, the 70Zr bulk rod, with [glass + IQ] phases obtained by annealing, shows a distinct increase in σy and σf to 1485 and 1575 MPa, respectively, as well as εp of 0.6%. Thus, the plastic Zr-rich bulk rods with glass, [glass + IQ], and [glass + β-Zr + ω-Zr] phase mixtures are encouraging for the future development of a new type of high-strength structural material.