What comes after CoPr?
Take another look at the definition of Core Practice:
Core Practice: the strategic decision to minimise cost in a discipline of the enterprise by implementing practices sufficient to (a) meet obligations and (b) to make processes work to a standard sufficient that risk (to the organisation and to people in its care) is reduced to some acceptable level.
Core Practice is just enough to make the Processes work and not put anyone (or the business) at unacceptable risk. We think that is a sensible and intelligent level for a business to aim for in non-critical areas of the business. We think there is too much emphasis on aiming for best practice in all areas: it is wasteful, distracting and a drag on the business.
But there will be parts of your business where it is strategically sensible, or essential, for you to aim for best practice. If you read that definition of Core Practice you will see there are some types of business that need to aim for best practice in just about all areas.
So CoPr is just the beginning. it says you have the business in control, you are doing what you need to be doing, and you are improving the areas that need to be continually improving. This gives you a foundation on which to build. Now you should look at your business and evaluate which processes need to operate to a more advanced standard.
Do you compete on quality? Then your quality control in particular and operations in general had better be more sophisticated. Do you deal in people's lives and welfare? Then you owe them the best you can be. Are you subject to critical scrutiny by the public or regulators? Then you want to point to exemplary systems. Do you already have processes more advanced than CoPr but you feel they are not as good as they should be?
In all these cases, you need to move on from here and go research what is regarded as best practice. We have provided references for best practice in many places throughout CoPr. Here are some of them: 0.11.17, 0.11.25, 0.11.36
CoPr shows you how to prepare a business case. Do one for any best practice proposal and ensure there will be a return that justifies the investment.