I had spoken to an agent on the IRCC helpline number and she had said that you can apply under multiple categories if you are eligible. I had asked specifically that I have my FSW application and wanted to apply under CEC . It is surprising that there are two statements coming which are contradicting
She sent me a mail which mentioned
Multiple permanent residence applications
If you are applying to immigrate to Canada, there are many
immigration categories available to you. Please note that the
Immigration and Refugee Protection Act (IRPA) does not prohibit multiple applications*.
If an applicant has more than one application for permanent residence (APR) approved, the responsible office will advise them to choose the category/class under which they would like to be granted permanent resident status.
Once permanent resident status is granted, any other pending APR should be withdrawn and the applicant notified.
*For example, you may apply simultaneously for two different streams in the economic class (e.g., Federal Skilled Worker Class and Provincial Nominee Class)