Do I have to go for F1 Visa stamping again if i want to do double masters but my visa is valid till 11/26/2020?

My Stem Opt denied on 2/14/19.I have applied some universities for Day 1 Cpt. My Sevis is completed and I have contacted the Immigration attorney.He suggested me to leave the country and can enter again once the new I-20 is issued from the new university.But in my Visa there is old Sevis ID.So, if i get the new I-20 there would be new Sevis ID or my Sevis Id would be transferred to the new university even after my SEVIS completed ? Will there be a problem in the Immigration at the time of entering back in U.S if I get a new Sevis Id ? or Do I have to go for new F1 visa stamping again for the new Master’s even though my Initial F1 visa is valid till 11/26/2020 ? and while entering again to US will the Immigartion hold me and ask many questions ? Please suggest me.

The SEVIS ID on your Visa is applicable only for your very first entry to US on F1 visa. If you transfer to other schools on F1 status, you do not need to re-apply for visa again. You can re-use the same visa as long as it is valid to re-enter US, provided you have a valid I-20 from a school in US. They may ask regarding your new school, admission, etc. Talk to your DSO at new school and inform them that you will be entering from outside of country and carry all the documentation for the same.