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Yes, it is possible, but it would be too hectic for you to concentrate on two subjects together.
CA course can very well be done along with your commerce graduation. However, you will have to wait till you complete your HSC Commerce with minimum 50% marks in aggregate. B.Com and CA course can be done simultaneously. And, in fact there are thousands of students who opt for the Company Secretary / Chartered Accountant / Cost Accountancy course alongside the graduation.
Do not neglect graduation studies at all. Your Commerce graduation is a solid foundation for your post-graduation ahead in life. It happens that since the professional courses like CA, CS, CWA require lot of hard work and time, students neglect the graduation studies. This should not happen with you my dear, is what I feel.
Therefore, score good marks in HSC Commerce, and then you can apply for Company Secretary Course and do graduation and CS course simultaneously.

Hi Manav,
As per the official website, the two-year full-time residential MBA at SIBM Pune is spread across four semesters and offering specialisations in marketing, HRM, finance and operations management. The structure of the programme is designed to give students the best in industry exposure and a nurturing classroom environment, to help them become the leaders of tomorrow, in the specialization of their choice.
Specialisations offered:
Marketing: A focused course structure equips those interested in this field with the skill set needed to understand, interpret and apply marketing concepts in live corporate scenarios. The students learn the practical applications of marketing principles through case studies, seminars, workshops, guest lectures and research projects.
Human Resources: This course provides students with the skills required for successful human capital management. It familiarises them with current corporate practices in the line. The course focuses on interpersonal and people management skills, to enable students to transcend the scope of Human Resource Management and become Strategic Business Partners.
Finance: This is designed to provide students with a strong base in applied financial management. It helps them in sound financial decision-making, providing a deep understanding of the financial aspects of the economy and the corporate world. The quantitative and analytic skills of the students are enhanced in the process.
Operations: Supply Chain Management, Logistics and Distribution networks have become huge differentiating factors for an organisation as it competes in the market. The course structure at SIBM Pune ensures that technological knowhow in these lines is integrated with current industrial practices to equip students to deliver beyond standard service levels for the businesses to grow further.

BBA is a Bachelors in Business Administration:
This study teaches the basics of business administration with respect to all the functions of a business like marketing, finance, human resource management, etc. It too has various specialisations namely Accounting, Entrepreneurship, Finance, Real Estate, Human Resource Management, International Business, Information technology, Legal management, Design Management, Management, Management information systems, Marketing, Operations management, Supply chain management, Public Relations, Aviation Management
BBM is a Bachelors in Business Management:
The main aim of this course is to make the student competent to take major managerial decisions, handle teams and manage the administration of a company on managerial level. It helps to develop skills required to deal with personnel and clients. Some of the specializations in BBM are Finance, Operations Management, and Management Information Systems and so on.
BBS is a Bachelors in Business Studies:
This is similar to the B.B.A. course but its focus is majorly in practical exposure rather than a theoretical study. In this degree various business courses are integrated with a realistic and industry-based focus in order to build sound business ideas within the aspirants. Aspirants can specialise in management, accounting, marketing and information systems.