Apple Music change billig date through switch of plans

Hi,

one idea I would like to change my Appe Music billing date to beginning of the month.

I have an individual subscription billed on 12th.

If I would upgrade to Family plan in beginning of a month, would that move my billing date to beginning of month, as I’m switching to the more expensive plan?

If yes, can I switch back to my individual plan on the same day and will it the be billed from then on in the beginning of the month? (For sure I have pay the family fee for one month)

Thank you