In this paper, details are given for the structural evolution of (Ti33Zr33Hf33)70(Ni50Cu50)20Al10, (Ti25Zr25Hf25Nb25)70(Ni50Cu50)20Al10, and (Ti33Zr33Hf33)70(Ni33Cu33Ag33)20Al10 amorphous alloys, part of wider program of alloy development by equiatomic substitution. All three alloys initially crystallize by forming a nanoscale icosahedral phase. However, at higher temperatures, their decomposition sequences differ significantly. The nanoscale icosahedral phase in the (Ti33Zr33Hf33)70(Ni50Cu50)20Al10 alloy decomposes into a mixture of Zr2Cu-type and icosahedral phases. This icosahedral phase still exists after heating up to 970 K, indicating a high thermal stability of this phase. The nanoscale icosahedral phase in the (Ti33Zr33Hf33)70(Ni33Cu33Ag33)20Al10 alloy also transforms into a mixture of Zr2Cu-type and icosahedral phase during the second exothermic reaction but then transforms into a mixture of Zr2Cu-type and Ti2Ni-type phases. The nanoscale icosahedral phase in the (Ti25Zr25Hf25Nb25)70(Ni50Cu50)20Al10 alloy decomposes into a mixture of Ti2Ni-type and MgZn2-type phases during the second exothermic reaction. It is concluded that the formation of the Zr2Cu-type phase retards the decomposition of the nanoscale icosahedral phase, which increases the thermal stability. In contrast, formation of Ti2Ni-type and MgZn2-type phases accelerates the decomposition of the nanoscale icosahedral phase, which decreases its thermal stability.