Upgrading a legacy network into a Software Defined Network (SDN) in stages, and minimizing the energy consumption of a network are now of great interests 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 only if they are adjacent to a SDN switch, and (ii) decreasing upgrade cost and increasing traffic demands over multiple stages. We formulate the problem as an Integer Linear Program (ILP) and propose a greedy heuristic called Green Multi-Stage Switch Upgrade (GMSU). Experiment results show that increasing budget as well as well the number of stages affect the total energy saved and the number of upgraded switches. GMSU produces results that are up to 5.8% off the optimal result. Moreover, on large networks, in which ILP becomes computationally intractable, GMSU uses less than 0.1 second to compute a solution.