RMAN - Incremental 0 and full backup

I have a very,very large database.

My plan is to have full backup on the 1st of the month and incremental for the rest of the month.

1st of month = incremental 0

the rest of the month = incremental 1

there is an internal reason for that.

however, we would also like to have full backup on the 7th, 14th, and 21st - but not part of the backup above, as in normal backup. as in normal backup and NOT incremental 0.

Question:

Are these full backup done on 7th, 14th, and 21st will mess with the main backup above (1st month incremental 0 and the rest).