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Yes, you can definitely take up a career in MSc Psychology after your B.Com. Though it is not directly qualifying you as a practicing psychologist, it will still help you to a great extent in building up a successful career in the desired field.
The most common route is through a Master's degree in Psychology.

Graduate programs are available in specializations like clinical psychology, counseling psychology, social psychology, or even industrial-organizational psychology in many universities. Coursework will be determined by the graduate programme and chosen area of focus. Bridge courses may be required to complete any undergraduate psychology deficiencies that exist.

Infact, with a BCom background in statistics, data analysis, and research methodology, you can make a great contribution to the research field of psychology or any other associated fields like neuroscience or cognitive science. Consider pursuing a Master's in these areas or research assistant positions in psychology labs.