Yes, this is very much possible. The Oracle binaries are shared but each database will have their own set of datafiles, controlfiles, passwords files, init.ora files etc.

You can create subdirectories for instance specific files

e.g:

/u01/oradata/DB01

/u01/oradata/DB02

Do some reading on the Oracle Optimal Flexible Architecture (OFA) here . This provides a standard for easily implementing multiple instances on a single machine/oracle home.