Can I change my shift at MSIT after taking admission?

Yes, you can do so. But you can only do that once you are in your 2nd year by the procedure known as the migration process. In this, you can change your college and shift too.

• For intra-college migration, i.e. migration within the college, you have to score at least 78 CPI, it is based on the credit score for each subject.
• In GGSIPU you get credit for each subject. The credit system is such that each subject has certain credits for e.g. Eco is given 4 credits, Accountancy 1, and so on. After the result, each subject is marked and multiplied against credits like if you scored 80 out of 100 in Eco, your credits are 80×4, i.e. 360. The rest of the credits are summed up to get CPI.
• CPI is used for up-gradation. All the up-gradation is totally based on 1st-semester marks. You have to fill an up-gradation form and have to submit it on the official website. There are usually 3-5 seats in each branch for up-gradation and for this you have to be among the toppers. 

Migration from one college to another does take place too. You have to score really well for the same. The information regarding inter-college migration can be found on the official website.