Can I delay my H1B activation date from 1 Oct 2016 to a later date (1 Jan or May 2017)?

I have a approved H1B petition with COS for this year and I am currently enrolled at a university with F1 status. I will graduate in Dec 2017 so I am thinking if I can delay my H1B activation to 3 months, I will be able to complete my Degree. I can convince my employer to delay the joining but I need to know it is even possible before I talk to them and their attorney. Since I am F1, I will have to maintain my student status till Sep 30 and that will require me to pay the full fee for next semester so it makes sense if I just complete the degree and then join.