As a holder of B.Com with ACCA, you don’t have to take additional exams unless you want to attempt some specific professional certifications. The ACCA qualification is quite broad and involves a comprehensive set of exams, mostly elite Fundamentals and Strategic Professional levels. After completing such tests, there are some practical experience hours as well as passing the Ethics and Professional Skills module to attain full ACCA membership, which you are qualified for after passing the ACCA exams.
Other certifications or advanced qualifications such as CPA or CFA would entail sitting for more exams. Such as, if concentrating in management accounting, one can sit for the CMA Certification Management Accountant exams. However, as you know, ACCA completed alongside a B.Com provides sufficient coverage for accounting and finance, so the remaining exams will differ based on the career goals in mind. Also consider pursuing a Master’s degree in Finance or accounting to make better use of your ACCA qualification.