No you can not, QBSE is very limited

QBSE does not allow for any new accounts (categories) to be created
QBSE does not have the class function
QBSE does not keep a customer or job listing
QBSE does not have a balance sheet so you can not enter the cost or the depreciation for […]

Resolution for 'capture business issue: 'Can you add project to QB-Self Employed? (if not, can you add a field to capture business division for self employed)' available: Yes.

The capture business 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 capture business issue yourself by looking for a resolution described in the article. If it is a complex capture business issue or you are unable to solve the issue, you may contact us by clicking here or by using other capture business support options.

For more information about resolving issues related to capture business in Quickbooks/QBO or to get support for the issue 'Can you add project to QB-Self Employed? (if not, can you add a field to capture business division for self employed)', click the link below: