Access to Revit Modify Geometry Functions

Hi Guys,
I am wondering if there is a way to access those Revit modify geometry functions
like cut, join, cope, mirror, split elements, etc.? it will be handy if those functions could
be added to our script so that these functions will be updated as well without going to
revit and do this manually? (please see attached image)

thank you,

Here is a limited python script, you still need to identify the elements to be joined and branch properly.

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thanks Japhy, looking forward for this area to be developed, cheers.