CFA

No, you can't opt for CFA along with MBA. You can pursue it separately, if it is required for your job, interest and future demand. CFA in India is offered by ICFAI Hyderabad. This course is designed with the consideration of Indian financial market. Whereas CFA USA is offered by some recognised training institutes from CFA USA. CFA USA is comparatively broad and vast than CFA India, as it is designed to cater the demand of international financial market. Any commerce or engineering graduates can pursue CFA USA or India. CFA USA offers core financial jobs then MBA finance. Some also prefers to pursue MBA+CFA. As the profile is concerned, CFA USA offers good job profile. As far as the salary is concerned, you can consider it as:(a) MBA=CFA in India.
(b) CFA offered by ICFAI.
To know more of MBA or CFA, follow the respective website of https://shiksha.com and CFA (USA).

Due to the program partnerships between business schools and the CFA Institute, there is now an efficient means for investment professionals to obtain both a graduate business degree and a CFA. Whereas it used to be adequate to obtain one or the other, this trend and the number of new investment professionals acquiring both graduate degrees and the CFA may ultimately require professionals to obtain both. Where the commitment was once two years of graduate school and four years of self study, now candidates that choose a partnering institution can perform a majority of the CFA commitment within their graduate school course work. Although it will still require an immense amount of commitment and discipline, an increasing number of institutions allow investment professionals to gain both breadth and depth of knowledge for all the investment management disciplines.