MOM did mentioned that we cannot start work with another employer during the period when we are serving notice (MOM – Termination with Notice).
Personally, I found it rather weird as it is not uncommon for people to have 2 jobs at one time. I had emailed to MOM for confirmation and their reply is as follow:
We are of the view that some employers do not allow their employees to work for another company whilst under their employment. Therefore, even when the employee is serving notice, they are still under the employment of their current employer and should not be employed by another employer without their current employer’s consent.
This seems to suggest that there is no legislation on disallowing one to have multiple jobs. However, if your contract of employment does mention that you are not allowed to work for another company during their employment, you are obliged to obey.