Yes you can. However, you should note that your EP can only be attached to ONE company. Singapore Company Act states that an Ep holder or an Local resident living in Singapore can register their own company. However, the Foreign Manpower Act states that a work pass holder can only work for one company. As MOM deems an inactive director of a company to be still considered as work.
If you would like to be a director of another company, you should still notify MOM and get their approval. However, for most cases MOM would reject unless you own a MNC who has multiple subsidiaries.
Despite all these negative information, there were some special appeals that we made for previous clients and was successful.
We would love to have a call with you to better understand your situation and advise accordingly. Do contact us at https://wa.me/6584833084