How to run multiple RAILS versions for a SINGLE website / project

I've inherited a RAILS 3.2 production environment which is 'humming' away nicely.

The client now wants another major piece of work doing but I want to do it in RAILS 5. The web address would be the same for both the old site and the new project. The new project would be additional functionality which would be accessed via the old site.

Any one know of a way of keeping the old site running whilst I develop and MORE IMPORTANTLY deliver the new work via RAILS 5. Eventually if this all works then I get the opportunity to migrate the old site to RAILS 5. However for the moment I need to serve up both RAILS 3.2 AND RAILS 5 from the same site.

All help/advice gratefully accepted with thanks