I was recently typed in the BE300 with a PIC limitation (must be under SOE supervision for the first 20 hours).

Currently, the aircraft is flown with another PIC on board, switching flying duties every few hours.

How would I log the initial 20 hours as sole manipulator? SIC or PIC?
How would I log the time, post 20 hours as sole manipulator?

I believe the -300 is type certified for single pilot.