Gspread to create a pivot table with index and columns on Google Sheets

Question

I am running this code below,

sh = gc.open_by_url('..........')
worksheet = sh.worksheet('Sheet1')
worksheet.update([df2.columns.values.tolist()] + df2.values.tolist()+df2.index.values.tolist())

df2 is a multi-index pivot table and running this code writes only the values and columns but does not include the index on Google sheets. Is there a way to include the index and the ability to change the format of the header on Google sheets?