Upgrading a legacy network to a Software Defined Network in stages, and minimizing the energy consumption of a network are now of great interest to operators. To this end, this paper addresses a novel problem: minimize the energy consumption of a network by upgrading switches over multiple stages subject to the available monetary budget at each stage. Our problem considers (i) bundled links that can be powered-off individually, (ii) decreasing upgrade cost and increasing traffic demands over multiple stages, and (iii) rerouting demands to an alternative path with a delay that is within a predefined limit. Additionally, the link load on the path is no larger than a given maximum utilization. We formulate the problem as an Integer Linear Program and propose a greedy heuristic called Green Multi-Stage Switch Upgrade (GMSU). Experiment results on five actual network topologies show that: 1) our approaches reduce the energy consumption by up to 73.98%; 2) rerouting traffic demand via longer paths improves the energy saving by up to 9.6%; 3) GMSU produces results that are at most 4.83% from the optimal result; and 4) increasing the budget and the number of stages affect the total energy saved and the number of upgraded switches.