Can I open more than one account when applying for an online brokerage account? 

Yes, multiple accounts can be opened on the same application form.  

However, the account types selected must be different and the account category (individual or joint) must be the same. For example, it is possible to open an RRSP, TFSA, and margin account on the same personal account application. 

See all the account types that can be opened online at NBDB.