| This paper considers the problem of upgrading a \textit{legacy} network into a Software Defined Network (SDN) over multiple stages and maximizing energy saving (ES) in the resulting upgraded network or hybrid SDN. In each stage, an operator needs to select and replace \textit{legacy} switches with SDN switches and seek to switch off as many cables as possible over each link. This paper addresses the said problem where it considers (i) the available budget at each stage, (ii) maximum path delays, (iii) maximum link utilization, (iv) per-stage increase (decrease) in traffic size (upgrade cost), and (v) each non SDN switch must comply with the Open Shortest Path First (OSPF)-Equal Cost Multi-Path (ECMP) protocol. It outlines a Mixed Integer Program (MIP) and a heuristic algorithm called M-GMSU. The results show that (i) MIP and M-GMSU achieve ES of up to $71.93\%$, (ii) using a larger budget and/or number of stages increases ES, and (iii) the ES of M-GMSU is within $3.55\%$ away from the optimal ES computed by MIP. |