SQL if last day of pervious month has value change the beginning date of next month to start from that day

I would suggest nesting EOMONTH() in an IF statement.

Not sure what table(s) you're working with, but general layout would be: IF(MAX(date_column) = EOMONTH(MAX(date_column), MAX(date_column), new_date)

Reference for EOMONTH(): https://www.sqlservertutorial.net/sql-server-date-functions/sql-server-eomonth-function/