I do not think the term née should ever be used twice in the manner you used in your question.

For someone born to a Brown family, who later married a Green, then a Smith then a Jones, I would say something like:

My mother Jill Jones, formerly Smith, before that Green, née Brown.

I do not think the term née should ever be used twice in the manner you described in your question.

For someone born to a Brown family, who later married a Green, then a Smith, then a Jones, I would say something like:

My mother Jill Jones, formerly Smith, before that Green, née Brown.

The term née means born, and a person can only be born once.