Two Oracle ORDS on one web server accessing one database
This can be done.  

Make a copy of the existing ords.war (call it, say, ords2.war) and just follow the same process that you would when creating your initial ORDS .war file. 
Just be sure to use different configuration directories for each ORDS .war file in order to avoid possible collisions.  

You name the two ORDS .war file differently in order to change the 'root'.  For example:

https://mywebsite.com/ords/...
https://mywebsite.com/ords2/...


has the 'root' of ords and ords2, respectively