QB Issue Resolution:

Yes you can,

  1. Click GST in the Left hand menu
  2. Click Edit GST and then Edit rates
  3. Click Add tax rate  

From there fill in the information for the tax code.

Resolution for Issue 'Can you add additional tax codes?' available: Yes (Solved).
Source: Intuit Community forum.

Can you add additional tax codes?: this issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the issue yourself by looking for a resolution described below. If it is a complex issue or you are unable to solve the issue, you may contact us by clicking here or by using other support options.

Support for additional tax
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Error Recovery for additional tax [Canada]
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