How do YOU capture multiple performances from Live's session view?

I'm currently trying to create arrangements based on session-view performances. Now I'm aware that multiple arrangements can't be captured within a single Ableton project (unless you simply position them in series along the timeline, if that makes sense).

So how do **you** do it? Rename a project every time you create a new arrangement?

It strikes me that, in a DAW so obviously aimed at live performance (hence the name!), there isn't a way to *contain* multiple performances within a project.

It's as if Live currently operates in two dimensions (the X or 'vertical' axis being session view, the Y or 'horizontal' axis being arrangement - a simplification, of course) when in fact it should have a third dimension - a Z or 'depth' axis that allows multiple arrangements to be 'stacked' so that you can select one from that stack as needed and work on it.