Upgrade from 3.0 to 3.1 and then to 3.2 - but keep 3.0 working

Hi,

I have 3.0.5 rails apps and they are getting older.
I'm planning the upgrade.

The guides recommend to go first from 3.0 to 3.1 and then to 3.2 so
that's what I will try.

But while I do the upgrade I want to keep the projects fully working and
probably even do some pushes to production with the current 3.0.5 apps.

So basically I want to do the upgrades in parallel without disturbing
the real apps.

I will use the same machine running Snow Leopard.

I use RVM for Ruby management.

Any recommendations how to setup this parallel upgrade? Is branching
actually an option, would so many changes (I guess ruby version, all
rails gems, gemfile, etc) fit as a branch?

Thanks.