Turbotax will not allow me to designate Third Party Designee on both Federal and State return. including going directly to the form

Go to Forms.  When in Forms mode open the Federal Information Worksheet (Info wks) on the left side of the screen when in Forms mode.  Scroll down to Part VI of the worksheet and enter the information for Third Party Designee.

If your state has the option for Third Party Designee on the state return, open the state Information Worksheet in the state section of Forms to see if there is a section available for entering Designee.