That looks like Fatsia japonica? If so you can cut back hard as you like and it grows new stems from below the cuts, as you can see in your picture. I've never tried cuttings from it but the RHS says semi-hardwood cuttings https://www.rhs.org.uk/plants/7147/fatsia-japonica/details so you'd probably need to let those new growths develop a bit more before taking cuttings from them.
The thing I know as cheese plant is Monstera deliciosa which is an indoor plant in the UK, and definitely not what's in the picture. Common names can be a minefield .
Doncaster, South Yorkshire. Soil type: sandy, well-drained
Posts