The purpose of this study to test an alternative treatment approach that involves giving participants radiotherapy before their mastectomy (preoperative radiotherapy) and performing immediate reconstruction surgery at the time of mastectomy. The immediate reconstruction surgery is called an immediate autologous reconstruction (IR) and is different than the standard reconstruction surgery people with T4 breast cancer have. IR is a surgical procedure where immediately following your mastectomy, the surgeon takes tissue from another part of your body and uses it to re-create your breast. The standard reconstruction surgery occurs later and can be done with an implant or tissue from your body. The main purpose of this study to find out if the alternative treatment approach shown above is feasible. The study will see how safe this alternative treatment approach is compared with the standard treatment approach.