Is there a reason to have a week or so in between steps? I don't think it's beneficial but it may not be harmful.
I do two step starters as a general practice. When the first step is done, I crash, decant, and add the wort for the second step. I time this to be ready for brewing when the second step is done. Usually, I will crash the second step the night before or morning of brew day.
Maybe a 5 days total in between starting and finishing both steps.