QB Issue Resolution:

You can not assign classes to a vendor or a customer

best you can do is in company settings>advanced>automation set the pre-fill forms with previously entered content to on and see if that helps somewhat

gear>your company>feedback and report/suggest it to the developers

Resolution for Issue 'I am a production company and we have over 300 classes. How can I pre set all 300 classes prior to entering a vendor?' available: Yes (Solved).
Source: Intuit Community forum.

I am a production company and we have over 300 classes. How can I pre set all 300 classes prior to entering a vendor?: 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.

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