Can a PEP holder start their own business in Singapore?

No.
The Personalised Employment Pass is not targeted at business owners or
independent freelancers, which means that PEP holders are not eligible
to start their own business nor engage in any entrepreneurial activity
in Singapore. PEP holders cannot be employed by their own company; the
PEP pass is only meant for foreigners who are employed by a third-party
employer.

Can a PEP holder work for multiple employers at any point of time?
Does a PEP holder need to leave Singapore after the expiry of the validity period?
Does a PEP holder need to obtain approval from MOM when switching jobs?
Can a PEP holder apply for Singapore Permanent Residence?
What is the minimum salary that a PEP holder needs to earn annually in Singapore?
What will happen if I didn’t meet the $144,000 fixed annual salary?
Can I get a multiple entry visa for the PEP?
What happens if I do not find a job for more than 6 months?
Who will sponsor my PEP and the Dependant’s Pass for my spouse or children?
Why do I need to provide the details of a local contact person for my PEP application?