A couple of bits you missed out are the MCC course which needs to be completed after everything else and the night rating.
You can combine the night rating as part of the PPL if your training provider agrees, likewise tou can do a 28 hour CPL with a multi engine rating included instead of the 25 hour single engine and then a sperate MEP.
In short the order is flexible but the rules which cause the problems are hours/qualification limits for entry to courses or for licence issues.
For example,
Cannot start ATPL ground exams unless you have a valid ICAO PPL.
Cannot start CPL course until you have 150 hours total time.
Cannot start ME CPL or ME rating unless you have 70 hours P1.
Must have 200 hours total including 100 hours P1, 10 hours instrument instruction, 20 hours cross country navigation for CPL licence issue.
Regards,
Obs