Philodendron selloum has frost/rot damage
I was given this plant a few days ago, and would like to save it if possible. I'm not entirely sure what kind of plant it is, but I believe it is something like a philodendron selloum (bipinnatifidum?). The plant was left outside in the cold for too long and seems to have rotted in many places. After being brought inside, it looks like some parts survived. The tallest stem seems to be rotten below where the leaves are, and many of the aerial roots also seem to be rotten. The soil the plant is in is very wet, so I am not sure what to do.
Can I cut off the top of the plant with the aerial roots and try to get it to root? Should I split off the smaller plants on the bottom? What kind of a plant is this so I can do more research about it? Thank you for your help!