Hope you are doing well - it's been a long time!!!
You can definitely drive the 'Delete' button using the 'Can Delete' attribute in CustomUI for this control. The 'Copy' can also be shown or hidden but it is static (can't drive its enable/disable feature using a property like you can for 'Delete'. Add will be enabled or disabled based on the subpart collection it is mapped to.
And of course, the other way to do it is use your own separate button for these 3 functions and drive them individually.
I know this is an old post and you've found the solution that works for you but just wanted to leave it out there for future reference.