Is there any differences or specific reasons between fine-tuning a base model and fine-tuning a fine-tuned model?

Hi everyone! I wonder what the difference between fine-tuning a base model and fine-tuning an existing fine-tuned models are.
Since fine-tuning a fine-tuned model:

  • creates a new model the same as what of the base model
  • restarts from scratch with the jsonl file used for fine-tune (not an amendment of the existing data)
  • costs the sames as what of the the base model
  • gives the same type of model name (unless you add a suffix)
  • gives the same results as fine-tuning a base model

So is it just a matter of preference or there are any specific reasons why we should fine-tune an fine-tuned model again.

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Not an answer to the question but
Can you please tell which model are you specifically trying to finetune? I tried all and I get

←[91mError:←[0m The specified base model does not support fine-tuning. (HTTP status code: 400)

I have fine tuned the Ada base model and then tried to fine tune the fine_tuned mode from that